Audio problem: In the kitchen scene, the instant the first velociraptor hops up onto the counters, it knocks off a large metal pot. There is no sound of it hitting the ground. (01:46:05)
Deliberate mistake: At the end of the kitchen scene with the kids and the raptors, one of the raptors chases Tim as he runs to the door. As it's doing this, Tim is running away with a bad limp, then as the raptor gains speed and is close behind, Tim's legs are perfectly fine as he sprints out the door and shuts it. (01:47:05)
Revealing mistake: In the famous kitchen scene, one of the Velociraptors leaps onto one of the counters and knocks over a metal pot with its left foot. The metal pot passes right through the CGI foot. (01:50:35)
Audio problem: In the scene at the end when they're in the ceiling then the raptor hits the roof top so it breaks and Lex almost fell to the ground. Well she's always screaming but look closely at the very moment when she falls, her lips don't fit at all. (01:51:30)
Revealing mistake: In the sequence when Lex almost falls from the hole in the ceiling, she looks straight back up at the camera. Rather than cut away from the stunt double at this point, they actually bothered to CGI the actress' face over the top so they could use the sequence right through. Unfortunately you can tell what's been done. (01:51:40)
Continuity mistake: When they are on the dinosaur's bones, one of the cords attached to the section that Lex is on comes out. The bone starts to fall and (for a fraction of a second) you can see that Lex lets go of it but in the next shot she is hanging on again. (01:51:45)
Revealing mistake: When the T-Rex has a raptor in its mouth at the end, the raptor disappears completely from the T-Rex's mouth for one frame. It's just after it's picked up - the T-Rex swings it left, then right, and as it swings to its left again the raptor disappears. If you want to be even more precise, there's a slatted/stepped white bit above the door - the raptor disappears about 3 frames after its foot moves above that white bit. (01:52:20)
Deliberate mistake: When the raptor breaks into the control room and is hopping around the computer workstations, we see sharp, distinct genetic coding projected from a computer screen and across the raptor's face (starting 1:55:50). Aside from the fact that computer displays have never projected focused images onto nearby surfaces, the projected text shown in this scene oddly reads from left-to-right, when it should actually be a flipped mirror-image (right-to-left). Spielberg probably realised this factual incongruity while filming but chose to use the left-to-right text for the sake of audience recognition, given that the multiple lines of "GATC" genetic code were already confusing enough. (01:55:50)
Continuity mistake: When Tim and Lex first arrive, Lex is wearing a purple tank top with a colorful design, and in the following scenes or even between consecutive shots her tank top changes to completely different designs, though it's the same style of tank top.
Continuity mistake: After the T. Rex rolls Explorer 4 upside-down with Lex and Tim inside, in the closeup when the dinosaur bites on the rubber tire we see the hub hole at the center of the wheel rim, but two shots later the wheel cover is back on the wheel.
Continuity mistake: While Lex and Tim are hiding in the kitchen, when the large serving spoon falls it cuts to the closeup of the two Velociraptors and the tall shelving unit has vanished, but in the next shot when the one of the raptors leaps onto the counter that tall shelving unit is back.
Revealing mistake: While the T. Rex attacks Explorer 4, when Lex and Tim are holding the roof up with their hands and feet, in one of the interior closeups after the T. Rex has lost its tooth we can see the metal post jutting out from the dinosaur's gum, to which the fake tooth is attached in the animatronic's mouth.
Visible crew/equipment: While Jophery's being attacked by the Velociraptors he's pulled out of Muldoon's arms, and when Jophery is yanked upward we can see the stunt cable at his side attached to the harness.
Revealing mistake: When the Dilophosaurus opens its crest, you can see the strings pulling it open. This has been fixed on blu-ray.
Visible crew/equipment: After Ian is thrown to the ground by the T. Rex, it cuts to Gennaro sitting in the collapsing bathroom hut, and we can see the set's scaffolding at the top of the screen. This is best seen on fullscreen DVD/VHS.
Continuity mistake: After Gennaro runs off to hide in the restroom there's a shot of the fence cables ripping apart, and in the following shot of the back of one of the Explorers note that it's missing its black roof vent (and rear wiper), but in following shots of Explorers 4 and 5 the vents are intact on both vehicles. Then just as the T. Rex starts pushing Explorer 4 upside-down its roof vent is gone (presumably, the vehicle missing the vent is a stunt vehicle).
Continuity mistake: When Ellie and Muldoon rescue Ian they leave him in Jeep 10 while they go looking for Alan and the kids, and after the closeup of the water filled T. Rex footprint showing an impact tremor, the next shot zooms in on Ian and we can see the driver's side-view mirror has no writing on it. When they're being chased by the T. Rex, in the shots from behind the Jeep we can see that both side-view mirrors have writing at the top and bottom (shown in closeup "objects in mirror are closer than they appear").
Visible crew/equipment: After escaping the T. Rex, when Alan and the kids climb the huge tree we can see a bit of what looks like netting at the top right side of the screen and also the set's scaffolding at the left side, then after the scene with Hammond and Ellie in the dining hall, when it cuts back to Alan and the kids we can see much more of the netting behind the tree set, at the top of the screen.
Revealing mistake: After the goat leg falls onto Explorer 4's roof, in the first shot of the T. Rex as she lifts her head to swallow the rest of the goat, when the camera tilts up the distinct outline of spray from the rain machine can be seen at the top of the screen.
Revealing mistake: After the T. Rex has flipped the Explorer upside down there's a closeup of Ian, and when it cuts to the T. Rex chomping away on the tire while the Explorer moves around, we can see that the acrylic glass roof is attached to the vehicle with thin cable wire - holes were drilled in the acrylic glass roof and sides of the vehicle.
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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