Continuity mistake: In 4-14 "Goodbye, Toby", Andy Bernard invites his parents to the going-away party for Toby Flenderson and introduces them as "Andrew and Ellen Bernard". But in this episode Andy tells Jim that he was originally named "Walter Jr." after his father and that it was changed when his little brother was born and the name Andrew was one that they got out of a baby-naming book.
Continuity mistake: In "The Alliance", Pam says that the next office birthday is Meredith's, but it isn't until the next month. Later, in "Survivor Man", it is said that Meredith's birthday is at the end of 'Birthday Month', when many employees have birthdays close together. It wouldn't be possible for Meredith's birthday to both be both the next office birthday but also at the end of the following month, which is stated to have many other birthdays in it.
Continuity mistake: When Jim and Dwight are talking about the activities for Kelly's party, Dwight is attempting (horribly) to blow up a silver balloon. Just after Jim finishes reading the list of proposed activities, Dwight says, "You're right, forget horse hunting, it's stupid." Immediately after he says this, the shot changes and he is now holding a brown balloon.
Continuity mistake: Episode 4 Season 1 "The Alliance" Dwight is hiding in a box in the basement when Pam comes down to the basement and pretends to make a secretive phone call. As she does so the box that Dwight is hiding in changes position on the floor, presumably so that the camera can catch the holes that Dwight has made in the box in order to breathe.
Plot hole: Oscar, Dwight, Jim, Erin, Kelly and Kevin are worried about a dog that have been left in a car, and that the dog will die. After some discussion, Oscar ultimately decides to smash the rear-driver's windows in order to give the dog some fresh air, yet there would be no point in doing this as the sun-roof is open, that's how Dwight pours milkshake into the car.
Plot hole: After Roy catches Jim and Pam too close for his comfort, Jim reveals the alliance joke. Then we see Dwight with the interview cam, while he has blonde hair. He had his normal hair just after the incident. There would be no reason for him to think that he needs to dye his hair at that point, since he had found out that Jim was messing with him.