Due to the fact that according to both the novel and movie, these "dinosaurs" are actually just human-engineered mutants, most of these inaccuracies can be explained in-universe as being just the results of the geneticist's tampering. The closest the films have come to acknowledging this is in Jurassic Park III when Grant says "What Hammond created was an island full of genetically engineered monsters. The real research is in the fossils..." -- the novel at least made it clear that the clones are just approximations, and not real dinosaurs.
This topic has became one of the most frequently discussed among paleontology enthusiasts, mostly because of how much our understanding of these creatures has progressed, and because there are many fans of Jurassic Park who refuse to accept that the dinosaurs in the movie are in several aspects inaccurate. Further, since to many moviegoers these films provide the sole source of information about dinosaurs, arguments about the topic occur frequently when a more knowledgeable person points out their ignorance. These inaccuracies aren't all mistakes. While some dinosaurs were indeed changed to make them better movie monsters (especially the raptors), most are the result of the relatively limited knowledge we possessed back when the movie was made. It should be noted that paleontology is an ever-advancing field of science, and as such, our image of these animals is always changing. A general overview on these paleontologic inaccuracies:
* The Tyrannosaurus is in fact one of the most accurate to appear in any popular media, including documentaries. However the shape of the head is too blocky and a bit wide, while the eyebrow ridges are far too pronounced (the animal in reality possessed only smaller "bumps" in front of the eyes). The arms appear to be just a tad too long and articulated, and the hands are able to twits. In reality, the wrists were fixed into a nearly immobile position, facing each other, but this is a relatively new discovery. As is the one made about the creature's hide: fossilized skin impressions show the animal had a heterogeneous, goosebumps-like skin texture, as opposed to scales, and this is evidence that, at least early in its life, T. rex was feathered. Scales were probably present on its throat-sac and on various parts of its body, though, like the underside of its tail. In the film, Dr. Grant states that its vision was based on movement, however we have no way of knowing this. We do know its eyes were very developed and that T. rex had great binocular vision, so it probably had no trouble seeing anything. Unlike the movie, the original Jurassic Park novel mentions that the inefficiency of the beast's eyes was actually due to gene-modification, and not a natural handicap.
* The Triceratops is also highly accurate, though we now know that its front feet had five toes instead of four, three of which were long and clawed, with the other two ending in stubs. These were also quite slender, and the back legs even resembled the legs of birds. In the movie, they are more elephantine. Also, a spectacular fossil find, an imprint of the skin of Triceratops, tells us that the scales on its belly were large and rectangular, while (most amazingly) the back of the creature may have had porcupine-like quills protruding from it.
* The Velociraptors in the movie became so embedded into public mind that a lot of people find it hard to accept that the real animals looked almost nothing like them. The raptors here are actually based on Deinonychus, a wolf-sized American dromaeosaur, rather than the Asian and turkey-sized Velociraptor. The book points this out, the movie does not. Even so, the anatomy of these "Deinonychus" is wrong in nearly every aspect. They are too big -- shown to be able to look a human right in the eye, however true Deinonychus would only come up to our waist or chest. This is because the legs of raptors were surprisingly short. Despite what the movie tells us, they (or at least the more advanced raptors, such as Deinonychus, Velociraptor and the gigantic Utahraptor) were bad runners, and likely ambushed their prey. Their claws weren't suited for slashing, as their inner rim was more rounded than sharp, meaning they used them for climbing and latching onto other animals, and then to puncture their throat. The famous Fighting Dinosaurs fossil, in which a Velociraptor and Protoceratops were found locked in combat at the time of their death, shows the raptor doing just this. Another theory regarding their killing strategy claims that they would have gone for smaller prey, and then clawed it to death while standing upright over it, using their wings to balance themselves and to keep other raptors away by forming a "shield" around their meal. It is unlikely that they used their teeth or wing claws for killing. The tail of raptors is shown as relatively short and bendy in the movies, but they were really much longer and quite stiff (the animals belonged to a dinosaur group called tetanurae, meaning "stiff tails"). They were flexible to a degree, but incapable of flailing around. The skull of the movie-raptors is blocky and stout, and doesn't match that of any known dromaeosaur. Their arms, or rather wings, are almost human-like. In reality, they were unable to rotate their wrists, meaning their hands were permanently stuck in a "clapping" position. They would thus have been unable to open doors. They also didn't hold their wings in front of their bodies. Paleontologists believe they held them at their sides and to the back. This made them more aerodynamic, and kept their feathers from touching the ground.
Most famously, raptors were feathered. Fossilized feathers show these were the same as the pennaceous feathers of modern birds, and not the type of primitive "fuzz" that a lot of other dinosaurs (for instance T. rex) had. Their arms were lined with long, sturdy feathers, the type birds use for flying -- many smaller raptors were indeed capable of using them to glide through the air, although not being able to lift them above their shoulder-line, they couldn't flap their wings. Raptors were covered head-to tail in feathers, and possessed fans on the end of their tail. Only the tip of their snout and their feet had scales, although some even had feathers sprouting from their toes. There is no evidence to suggest raptors were pack hunters. This theory was based on several Deinonychus skeletons that have been discovered together with the skeleton of a herbivorous dinosaur, but recent studies indicate that these weren't found together because they formed a pack when alive, but because they came to feed off the carcass, and subsequently fought over it, during which many Deinonychus were killed -- their remains also show signs of scavenging, meaning they could even have ate each other. Also, while raptors were probably smart for dinosaurs, they likely lacked the necessary intelligence needed for coordinated assaults. However there exists a fossil trackway that shows a bunch of these animals walking in a group, so the question of whether they were social or not has yet to be cleared.
* The Dilophosaurus is another animal whose appearance the movie famously changed. For starters, it's far too small -- true Dilophosaurus were about 6 m long, and as tall as a person. The one in the movie could be just a juvenile, though. The iconic frill was, however, only made up by Steven Spielberg, and its venom-spitting ability is also artistic license, used to demonstrate what little fossils actually tell us about dinosaurs. Accordingly, neither of these traits have any scientific basis. Nor do they make logical sense: if a carnivore attempted to attack another animal in this theatrical manner, the prey would have plenty of time to just run away. The shape of the animal's head is also wrong: it's short, stout and compact, whereas the jaws of Dilophosaurus were famously thin and long, and the upper jaw had a small notch at the tip, which the movie version lacks entirely. Likewise, the palms should be facing each other, and the animal had four fingers, not three.
* Brachiosaurus is shown chewing by moving its jaw from side to side, which is a motion the skull was incapable of doing. Further, its teeth were only meant for stripping off branches, while the stones the animal swallowed did the grinding. Brachiosaurs were the sauropods least capable of rearing up on their hind legs, especially as their backs sloped toward their rear, and because their hind legs were shorter than their front ones. On their front feet, they only had one claw, while the other four fingers were reduced to mere stumps. Sauropods were famously believed to have had their nostrils placed high up on their foreheads. But the latest studied show that they had fleshy tubes running down their face, and the nostrils were located on their noses. It is worth noting that the Brachiosaurus here (as well as in just about any popular media) was based on fossils that have since been reclassified to a related genus, Giraffatitan, which was for almost a century regarded as a species of Brachiosaurus. We now see them as different genera, and the build of Brachiosaurus would had been slightly different -- its torso would have been more tubular, for example, and the "bulge" on its forehead would have been less pronounced.
* Gallimimus should be fuzzy, with the arms being lined with sturdy wing feathers, and their palms should be facing inward.
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