Many of the continuity "mistakes" were included intentionally by the filmmakers and were meant to be subtle and funny, including Neil's hair in the motorcycle chase scene and the differing level of completion of the blanket that Nancy is knitting when she gives Beth and Henry the library advice.
When Coop finds Katie talking with her boyfriend in his cabin, Coop talks with her while standing in the cabin doorway. Shots of Coop framed by the doorway show that it is raining outside, but it is not raining before or after.
During the breakfast scene, Beth is sitting at the table with Gail (Molly Shannon) on her right and Nurse Nancy (Nina Hellman) on her left. Later on in the same scene, when Beth talks to Victor, Nurse Nancy is sitting on her right where Gail should be.
In the scene where Gary is peeling potatoes outside, both his hair and Gene's facial hair are noticeably longer than in any other scene in the movie. It would appear that this scene was filmed much later than the rest of the movie.