Continuity mistake: At the end of the film when David Duchovny and Orlando Jones go up the ladder to squirt the Head and Shoulders into 'the hole', Orlando Jones gets sucked up into the alien and when he is pulled out he is covered in slime from head to toe, (including his glasses), as is David Duchovny. However, in the next shot of them going down the ladder there is no slime on them at all. In the next shot when they are standing at the bottom, while the truck pulls away, neither of them have much slime on them, and Orlando Jones' glasses are completely clean. The amount of slime they are covered in changes throughout the next few shots. (01:32:50)
Plot hole: Because humans have a layer of subcutaneous fat under the skin, the bug that travels under Harry's skin would have caused not only significant damage but an amazing amount of pain while moving around. There would have also been severe internal damage caused by the bug if it traveled into his colon where they ended up removing it from.
Revealing mistake: When Harry and Ira take the students to the cave to excavate the meteor, pay attention in the first wide-shot back in the cave where you can see smoke/vapor on the ground. You can see a small patch at the very bottom of the meteor where the smoke is being pumped onto the ground, likely by a concealed smoke-machine either inside of the prop meteor or just underneath the set. You can see the smoke sort-of "churning" unnaturally at the base of the meteor as it is pumped onto the ground, giving away the effect. And to avoid any corrections, yes they say that the area is being adapted by the microbial life the meteor brought to earth and developing a mini-atmosphere in the cave... but this is an unintentionally visible effect. The atmosphere/smoke/vapor wouldn't be all coming from one single tiny spot at the base of the meteor, and it wouldn't be billowing and churning like smoke being pumped from a smoke machine.
Character mistake: In the scene where the gorilla type creature has taken out one of the security cameras, they say "one of the creatures just destroyed video four" but if you look, camera four is intact and it is camera two that has been taken out. (01:08:05)