At the beginning of the film when Doyle was hit by the book and flew backwards into the book shelf, the shelf was partially destroyed. But when his girlfriend slaps him and stands up, the shelving unit is completely untouched.
Near the beginning of the "safety Dance"/rebuilding the dome sequence, part of the desert area is shown and there are several party goers still sleeping on the ground. This is several days after they re-closed the dome, and these people are never seen again in the movie.
In "the book scene", when Bud is lining up in the hallway the camera cuts to Doyle and we can see he is standing with the coffee table lined up right next to him with no room to pass him. As Bud hits him, the camera changes to a view of him from behind, and we can see Bud has plenty of room to get past Doyle as the coffee table has moved.
When Bud and Doyle try and get out the main exit (Sherman tank scene) Olivia says that nothing comes in our out, not even air. However, there is a large crack under the "airtight" door that is letting light in.
Dr. Romulus refers to the butterflies as a rare species called Lepidoptera. Lepidoptera is the Latin name that refers to the order of insects that butterflies and moths belong to, not an individual species.