Continuity mistake: When the bird first hits the RV, a blood stain is visible on the windshield. But on the exterior shot of the RV as it stops, the blood has disappeared. (00:26:50)
Continuity mistake: The shot of Graeme and Clive's RV crashing into the side of Haggard's car is used twice.
Continuity mistake: When Jason Bateman does a high-speed u-turn (hand-brake turn) on the highway, the camera cuts to a close-up of him driving. You can see that he is driving on the right side of the car, instead of the left side.
Continuity mistake: When Clive and Graeme pull over after Paul wrecks the black car, headlights can be seen just coming over the rise behind them. In the next shot as they clamber out of the RV, the road behind is suddenly deserted.
Continuity mistake: When Graeme gets shot towards the end of the movie, there is a large bullet hole, with visible blood, and a torn jacket where the bullet went in. Later when Paul is getting onto the space craft waving goodbye, the bullet hole, blood, and suit are now all gone and cleaned up. As if it was never there. Taking into effect of what we know, Paul can heal, but I don't think he can mend clothing as well. (01:29:50 - 01:42:00)
Revealing mistake: When the car Paul is driving spins out of control and flips, the roll bar is visible through the back window.
Plot hole: The huge explosion that rips through Tara's house isn't very likely. She only left the stove on for a short while, and if there was really a massive concentration of gas as depicted by the explosion, the Agent who fired the shot that triggered it should have collapsed from inhaling so much gas.
Continuity mistake: In the scene where the two friends order at the diner his pancakes have whipped cream on them he puts his arm in the whipped cream yet in the next shot it is undisturbed.
Other mistake: When Graeme is convincing Ruth to go with them and she says "Where would I sleep?", you can see her left eyeball through the dark lens: it moves as she looks to her right twice and then back. In the next scene, it is shown that she doesn't have a visible eyeball in her left eye. (00:45:05)
Continuity mistake: As Nick Frost and Simon Pegg are running away form the fireworks shooter, they both have their head lights on. As they reach the others Nick removes his and in the next shot he removes it again. Simon has his on in the first shot, it has then disappeared in the next. (01:18:55)
Continuity mistake: In the scene after Graeme rips the sticker off the RV, Paul is wearing a seat belt, in the next shot he is not.
Continuity mistake: In the scene at Ale inn where they are deciding on which banner, there is a gentleman sitting at a table in the background. He is served by a waitress, there may be another person there. He and the waitress chat while it looks like she is pouring coffee. Next cut to Simon and Nick shows that the waitress and customer have vanished. (00:08:30)
Factual error: When Jason Bateman first meets the rookies at the roadblock, some Saguaro cacti can be seen in the background. Saguaro are not indigenous to Nevada.
Continuity mistake: The rude drawing that Buggs picks up when it flies off the RV has creases and damage to the holes at the top left (above the letters F and U). When Haggard finds it in Buggs back room those same holes are perfect. (00:39:10 - 00:43:20)
Revealing mistake: Look closely during Clive's argument with Graeme. You can see Ruth's left eye which is supposedly blind, actually appear normal behind her glasses' dark lens.
Continuity mistake: The broken katana at the end of the film keeps reappearing on his back in some shots, but in other shots it's just an empty holster.
Continuity mistake: After Graeme and Clive leave the diner, Graeme gets in the RV after he said he was putting the alien on board sticker on the back. But after they crash into the pickup truck and drive past the ET highway sign, the sticker can't be seen on the back of the RV. Neither can the black mark that is left behind when Graeme later removes the sticker after they meet Paul.
Continuity mistake: In the scene in the RV where Paul and Ruth are arguing about religion there is a fly swat and a green flowery oven mitt hanging on the hooks on the wall behind Ruth. In the next shot, she has the fly swat in her hand but the green mitt has disappeared, and it isn't she just knocked it down out of shot, because later in the same scene when we see Clive driving and he says "Oh yeah" it can be seen hanging there again. (00:41:25)
Chosen answer: The movie "Paul" was riddled with inside jokes and homages to classic science fiction and adventure movies and tv shows, so it would not be surprising there would be a reference from an Indiana Jones movie. Also, Paul is, indeed, "short" with a "round" head.
Scott215