Corrected entry: During several of the episodes, the cuts in the table from when Jeff hit it with an axe are seen. But during the credits sequence of the first episode, we Annie plastering the holes. So how did they get back?
Corrected entry: Pierce tells the Biology teacher that the study group members are the only people he has told about having sex with Eartha Kitt in an airplane bathroom. However, in 3.04 'Remedial Chaos Theory', Pierce tells the group about Eartha Kitt for the first time. Also, in 3.03 Shirley calls Britta's lighter her "marijuana lighter", but she doesn't find out about Britta smoking weed until 3.04. These errors are due to 3.03 and 3.04 being aired out of order according to their production, and have been acknowledged and confirmed by creator Dan Harmon himself, but they still count as mistakes.
Correction: Those two revelations only happened in the alternate timelines, not in the main timeline. In the main timeline, Pierce was about to mention Eartha Kitt, but was stopped (all he said was, "Airplane bathroom..." and was cut off), and Britta's smoking was never seen. Additionally, in the alternate timelines, nobody says or implies that it's their first time hearing about Earth Kitt (in fact, in one of them (the Darkest Timeline), they imply that they HAVE heard the story before, because Pierce mentions Eartha Kitt but not sex or the airplane, and the group is still disgusted) And Shirley was ranting about Britta's drug use which can very well be attributed to learning that the whole group decided not to eat her baked goods. It can only be assumed that the revelations came some time before episode 3, off screen. The mention of them being shown out of order is irrelevant given these facts.
Correction: All she did was fill in the holes to make the surface even. So there are still visible marks where the table was hit with the ax. The only way to make them go away entirely would be to paint the whole table, which we never see them do.