Audio/visual unsynchronised
When Jay and Seth make it to Heaven and see Craig, Jay starts yelling, "Yay!" as both Jay and Seth run to Craig. Jay yells the whole time until they reach Craig, but when they reach him the audio for Jay is still going while his mouth is closed.
Continuity
When the possessed Jonah Hill violently vomits on James Franco and Seth Rogen, the penis statue can clearly be seen intact. This is the same statue that Emma Watson beheaded earlier in the film.
When Jonah Hill vomits on Seth Rogen and James Franco, they are completely covered in vomit. In the next shot their hair is dry and their t-shirts are only a bit wet.
When Jay and Craig are running from the dog-like demon in the neighbor's house, Craig saves Jay by pushing him out of a glass door. As Craig is jumping into Jay he is securely wearing the backpack full of food but when they crash through to the outside the very next second he is not wearing it.
Crew or equipment visible
When the beginning scene cuts to the hand-held camera following Seth Rogen, the camera which was filming Seth and Jay walk away from their meeting place can be seen.