Where to start? I'd say, with the comment made on a paleobiology blog; "...that British-made sci-fi sitcom."
The show ran for five seasons and spawned a half-dozen novelizations and original books as well as a short-lived Canadian-made spin-off. The elevator pitch was likely something like "Torchwood with dinosaurs" and at that shallow level it delivers; a photogenic cast with entertaining dynamics having exciting encounters with paleontologically-based monsters-of-the-week while through the seasons slow revelations of a larger plot evolve.
Immediate plus point in that the prehistoric creatures presented -- although weighted heavily towards large and fierce apex predators -- were interesting and even obscure. It took them a long time to introduce a spinosaurus, and many of the beasties are various therapods somewhere along the long and murky trail from synapsids to early mammals.
And another in that status quo is far from god. They killed off major cast members and changed the methods and even focus multiple times. They also changed the style of the show along the different seasons, although this was even more of a mixed blessing.
First the science stuff. They obviously did their research, but they openly admit that pretty much everything was scaled up significantly. Their models were largely adopted from "Travels with Dinosaurs" which already put sensationalism and haste over accuracy, and in several episodes they drop even that pretense of academic support; one of the wee beasties is apparently drawn from the flights of fancy of long-time kook (but excellent illustrator) Dave Peters.
That said, paleontologists are a contentious lot. I have only anecdote but (outside of little incidents like Tycho Brahe's nose) it certainly seems that they are the most likely of the sciences to have their heated discussions break into fist fights. Their discussions and conventions seem rather more rough-and-tumble than you'd expect from, say, theoretical physicists. So one can't fault anyone, but particularly not a one-hour entertainment television slot, from simplifying the complex, contradictory and contentious state of our ever-increasing knowledge into something more coherent.
Actually, though, this is one of the major problems I have with the show as a presentation of science. They are far too certain. Especially since soft tissues are poorly recorded and details like coloration (not to mention wattles, frills, fronds, hair, feathers, etc.) are quite extrapolated, I find it hard to believe that every creature encountered even in the dimmest light is going to be amenable to spot identification.
Even the Spielberg trio did better than this; people in those movies were constantly being surprised by the live creatures, and as well taking the opportunity to explain that there were numerous contending theories before this new observation. In "Primeval" they do one internet search (or just pull up the information from their own memories) and immediately they know the body plan, habitat, and basic behavior.
Of course, in the show, pretty much all the behavior is stereotyped and simplistic. I haven't even seen the show draw attention to the difference between an ambush predator and a pack hunter. I don't even know how to classify the typical behavior shown in the show, except as Hollywood predation; they don't even seem to get around to actually eating their kills half the time, and are easily distracted from an easy kill or even a fresh kill by an active but distant distraction. Unlike natural behavior, even a wounded prey at their very feet is apparently less attractive than one that is yelling and waving sticks at them and running away at high speed. Maybe the chase instinct was overdeveloped in prehistoric times?
They do sometimes mention the specifics of the environment a creature has evolved in, or the special adaptions -- one may climb well, another can't tolerate heat, etc. But this is quite shallow, and tends to show up in the show as a Special Weakness they can exploit at the nth hour. So each encounter becomes largely formulaic, right down to the "Snarl for a while then leap" behavior of everything from large herbivores to (marine!) tube worms.
The rest of science gets even shorter shrift, of course.
In the mythos and development, this is where the evolving nature of the show shines. The first episode revealed a cluster of lights appearing in the Forest of Dean, which on investigation was a temporary portal to the late Permian. Unfortunately a local gorgonopsid had also strolled through the portal in the other direction, and was feeding on the local Brits.
This rapidly set a framework where our reluctant hero paleontologist Cutter, a geeky lab assistant, a herpetologist from the local zoo, and an experienced tracker/hunter, became the scientific advisors to a small military force run in top secrecy from some ministry or other that had the right combination of resources and luck to be saddled with this. Their basic goal was to learn when an anomaly opened, and to track down any incursions (aka local wildlife wandering in from whatever era was on the other side of the anomaly).
They early on lampshaded this rather bizarre team and the way our civilian stars soon took over the show by pointing out that they seemed to be very, very good at the job. Interesting was also the conservationist approach of Cutter, who whenever possible returned the animals to their own time. His attitudes seem to have infected the others, who rarely carried any weapon. (They preferred to MacGuyver their way around, but truth be said, their major approach to most problems seemed to be waving their arms shouting "Over here, ugly!" in turn, confusing the poor beastie until they could do something more effective.)
The mythos deepened when Cutter's wife was discovered still alive. In fact, very much alive and enjoying herself skinny-dipping in the Jurassic and stealing eggs for breakfast from pteranodons. Or whatever. She appeared to know a lot more than they did about where and when anomalies would appear, seemed to have the ability to move freely about time, and wanted Cutter to drop his work saving people from rampaging coleosaurs and join her sunning on a rock in the triassic instead.
And then came Season 2. Helen Cutter's interference caused a change in time, and Cutter came back to find the team now housed in the high-tech "ARC." Geeky Conner had gotten his first upgrade as well, now being a genius polymath who was able to quickly invent an anomaly detector. They all got haircuts, nicer jackets and more hair gel. And Helen got her own upgrade to, well, basically insane.
So core cast member Claudia vanished between seasons due to be edited out of history. Stephen bought it stopping one of those typical only-in-the-movies meglomaniacs who thought he could rule the world if he only had enough raptors with radio control collars (actually, Future Predators with fancy mind control things also from the future, but same idea). And Cutter got shot by Helen early into Season Three.
Egyptologist (and also mythology, language, cryptology, history and ethnology polymath) Sarah joins the cast straight from the Mummy Room at the British Museum, with strong hints that many of the creatures and stories from myth were the result of various anomalies, and some cultures may have understood and even exploited the things -- an intriguing new direction that lasted for all of one episode then was summarily dropped, with a brief encounter with a St. George like 14th-century knight the only sop to this potentially interesting angle.
Helen Cutter goes the rest of the way to madness and tries to single-handedly wipe out the Australopithicines (apparently Johansen didn't notice Lucy had been poisoned...) but is stopped at the climax of Season 3. And at least as of mid-season 4, all of her mysterious future technology, clone armies, and so forth died with her.
Season 4 brings on yet another batch of new characters, and gives our surviving starting roster of Connor and Abby even more buffs including a relationship upgrade. Sarah dies off-screen between seasons, and Danny only comes back briefly. And then the series veers off into yet another nutso industrialist trying to rule the world through Weird Science (although to his credit, he basically meant well).
All through this, the meat is still the monster of the week, but the format and feeling of these chases changes quite drastically, as does the overall flavor of the series. In general the earlier series are more serious, and the characters more grounded. Kudos again for not staying in status quo, but if they did my dream team would still be the original team, plus perhaps Sarah. Nuancing it, I'd take Cutter before his Season 2 haircut, Connor after his upgrade, Abby from her earlier cute phase but without the designated victim baggage of the first couple seasons. And more Rex.
But as for the show that never was... Well, the idea isn't bad. It is nice that someone thought about the implications of opening random doorways to another time, but it is a little sad that the major threat that wanders through happens to be the local apex predator more often than not. Population pyramids alone would suggest that for every Serengeti Lion, you'd see dozens of antelope first. Apex predators can't be the only creatures curious enough to go poking their head into the funny light!
And as visceral as two hundred pounds of snarling sabre-tooth meat is, the true risk of such passages would be such things as invasive species. Oddly enough this is never really mentioned. Although I do have to say it is harder to dramatize the existential threat posed by the Permian-incursion equivalent of rabbits being introduced to Australia.
The lack of any truly interesting or distinguishing behavior or other characteristics is also disheartening. There were exceptions. A few herd animals, some burrowers that were dangerous only by accident, a couple of parasites and even a fungus. And various aquatic beasties that had to be dealt with in mostly wetter ways.
As with all such gates through time and/or space, one has to wonder what would be the result if they weren't treated as one-off events kept hidden and access strictly controlled; if they were opened to market forces, with massed exploration, trade, tourism, exploitation of resources, and a whole host of entertaining problems resulting from that. That would be a very, very different show all right.
Another entertaining thought the series sort of addresses by default is that the toughest predator of the Cambrian is not necessarily tougher than a modern wide-mouthed bass. Now, evolution has no arrow. It is not intentional nor directional, and adaption is merely towards the optimum available trade-offs to the current environment.
That said, between us and the top of the food chain of a Permian ecosystem is 250 million years of tinkering around with new options in biology -- down to the molecular level, with better enzymes for muscle recovery, faster nervous conduction, etc. It would be easy to go too far with this -- and yes, humans are specialized largely in flexibility and plasticity, not in being Superman -- but I'd like to see someone play with the idea.
I mean, thanks to our extremely advanced thermal management system, not only can we remain active in very cold weather (large beasties get an advantage due to sheer bulk in this, so don't taunt the dinosaur caught in a snowstorm just on the basis of this) but on the right day we can run to the ground anything lacking sweat glands. Especially given that most predators emphasize the prey that is easy to catch over the prey that appears to be getting away, I'd think a lot of these encounters in any real biological and behavioral world would involve human sprinting like mad and early reptile breaking off pursuit after a short dash.
So I don't find it particularly astonishing that a well-adapted Terror Bird doesn't end up being fairly well matched against a human -- when said ornithoid is in unfamiliar (and cramped) human-built spaces and said human has the local equivalent of pointed stick. The lowly baseball bat or golf club may look a little ludicrous but it combines strength and a well-designed center of mass with a low enough weight to let it get up a pretty impressive swing.