Visible crew/equipment: After Alan, Ellie, Lex and Tim run into the control room Alan tells Ellie to boot up the door locks, and when the Raptor opens the door Alan drops his gun and we can see two distinct reflections on the glass - the Raptor's puppet head on someone's arm as it pushes on the door from outside the room, and also the reflection of a crew member (presumably standing in the camera area).
Visible crew/equipment: While Alan and Ellie are trying to keep the Velociraptor out of the control room Lex is on the computer trying to find the file to restart the security systems, and after Tim shouts, "Come on Lex!" it cuts to a closeup of the Raptor's claws at the door and we can see the crew member's head.
Other mistake: When Dr Grant and the children reach the perimeter fence, Dr Grant tries to see if he can fit through, to no avail. When he and the kids start to climb, however, it is quite obvious that both Tim and Lex would have been able to crawl through quite easily, and that only Dr Grant should have had to climb over. Partly this links to the mistake here, where the holes in the fence are much bigger in the first shot, then when he tries to widen them he's holding a different part of the fence where they're smaller.
Continuity mistake: While Lex and Tim are hiding in the kitchen, just as the Velociraptors come in Lex tells Tim to follow her, and when they turn into the aisle there's a stainless prep unit with no open shelves right beside them at the end of that aisle, but after the closeups of the Raptor's claws, when the kids continue to crawl away that prep unit has oddly vanished - the last unit in that aisle has shelves, and then it reappears when Tim sits under the utensils.
Continuity mistake: When both Explorer vehicles are parked at the paddock, in the shot of the goat being raised to lure the T. Rex, the "No! Feeding..." sign is permanently affixed to the front of the concrete wall, but in the previous and following shots that same sign is affixed to the angled top part of the wall. Later, when the power goes out, that sign is once again affixed to the front of the concrete wall.
Visible crew/equipment: After the T. Rex flips Explorer 4 upside down it continues to attack the vehicle with the kids inside, and when it cuts to the T. Rex chomping on the tire, as the vehicle moves around we can see the hanging bundle of wires leading up through the window and also what looks like a crew member or something else that shouldn't be there, outside the vehicle behind Lex. Even if the wires were to belong to the Explorer they shouldn't be leading up and outside the way they are.
Continuity mistake: After Hammond's chopper lands causing winds at the dig site in the badlands, when Alan opens the trailer door the rock hammer is hanging from his belt, but in the interior shot as he walks in the rock hammer has vanished.
Visible crew/equipment: When the Explorer vehicles begin the tour, we hear the voice of Richard Kiley explaining that the first dinosaurs on their tour are a herd of Dilophosaurus, and in the next shot of Alan the reflection of the camera can be seen on the surface of the window.
Continuity mistake: After Dennis has stolen the embryos, when he reaches the first gate he gets out of the Jeep then uses the manual override to unlock the gate, and in the exterior shot when Dennis walks back to the Jeep his door is wide open, but in the next interior shot his door's closed and he even has difficulty opening it.
Continuity mistake: In the scene with the T. Rex breaking through the glass roof, as the glass breaks one of the rex's front teeth breaks off and flies backward. On the next close-up of the dinosaur's mouth, the tooth is still missing, yet it is back in all shots after that.
Visible crew/equipment: In the scene where Grant and Lex are hanging from the fence cables on the wall in the Tyrannosaur paddock they start swinging back and forth to avoid the truck that is about to fall on them. Look closely in some of the closeup shots, you can see that the cable that Grant is holding on is actually a safety rig. The harness straps are visible.
Visible crew/equipment: When the two Explorer vehicles begin the tour and drive past the huge automated wood doors, if we look at the area between the two doors just as the doors are shut we can see someone's arm come down from behind the door on the right, presumably to keep both doors properly closed for the shot.
Revealing mistake: While the T. Rex attacks the Explorer that Lex and Tim are in, during the stunt as the acrylic glass roof comes down on the kids in the interior shots, the strip of duct tape falls through the opening and dangles from the roof of the vehicle - presumably the tape was holding the acrylic glass roof in place before the stunt.
Continuity mistake: Right before the T. Rex breaks out of the paddock there's a shot of the back of Explorer 4, and the rear windshield wiper is gone, but it reappears, vanishes, and then reappears again during the T. Rex attack.
Continuity mistake: When the T. Rex escapes its paddock and then Tim tells Lex to turn the light off, in the interior shot after Tim closes the vehicle's door, the plastic piece (used for seat belts) anchored to the panel between the windows vanishes inexplicably leaving just a hole, and when the T. Rex roars Tim covers his ears and there's some kind of small plastic on that hole.
Continuity mistake: After Alan pulls Lex out from the overturned Explorer and the T. Rex spins the vehicle around, in the closeup shot from behind Tim while he's still inside the Explorer, as the T. Rex leans down facing Tim we can see one of the lower front teeth is missing, but it's back in the following shots.
Continuity mistake: When entering the visitor centre, Ian goes from the side of Hammond to the back of all the characters without a chance to move, in a single shot.
Continuity mistake: When Grant grabs onto the electric fence, his hands are a short distance apart and there is a set of vertically positioned wiring in between his hands - the warning sign is also barely covering the "hole" in the wires. A couple of shots later, without letting go of the fence, his hands are much further apart and there are now three sets of vertically positioned wiring in between his hands. The angle of the wires also changes, and the sign is now well into the "hole", very near his hand.
Character mistake: When Nedry is stealing the embryos, an extra "n" is missing on the label "Tyranosaurus".
Continuity mistake: At the site of the T-Rex attack, Ellie and Muldoon help the injured Dr. Malcolm into the back of the Jeep, before Ellie goes looking for the other Explorer. Muldoon hears the T-Rex approaching and shouts "Ellie, come on!" but Ellie spots the Explorer over the wall and (in the next shot) she and Muldoon (heard but unseen except for his torch beam) have left Dr. Malcolm alone, somehow descended the high wall, and are running up to the wrecked Explorer. There is no implied time gap between the shots as they could hear the T-Rex was approaching before they did (or did not) descend the wall and later the T-Rex is almost at the Jeep (now in a different location) and Dr. Malcolm is urgently calling them back.
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.
raywest ★