Revealing mistake: When Tim is looking at the 2 cups of water vibrating due to the T-Rex's stomping, you can see a very small dark spot at the bottom of the cup, which is actually the knot of a guitar string that was plucked to create the vibration effect.
Continuity mistake: When Nedry's car is stuck in the mud, he goes out front to grab his winch and pulls out a fair bit of wire. In the next shot, we see that he has a lot less wire than before, even though we never heard the winch retract.
Continuity mistake: When the baby Dinosaur is hatching, her arm comes out but in the very next shot it's her head that is coming out. (00:27:30)
Answer: They are not paleontologists, just people interested in dinosaurs. It is common for museums and other scientific organizations to offer the general public an opportunity to participate in a real paleontology dig. For a fee, they become an exhibition team member for a period of time, learn about dinosaurs, help excavate fossils, and so on. This is likely how Dr. Grant (or his institution) supplements his research funding.
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