Goof (revealing mistake): During the first Scrabble game, Dilmom puts down the word "quixotic" as the second word of the game. Given Dilbert's first word is "it", it is impossible for Dilmom to have put this word on a Triple Word Score. It can be easily proved with a Scrabble board. Dogbert's claim that his word "quizzing" scores 188 points is also false, but given that Dogbert is cheating in the first place, that is more likely to be Dogbert making things up than an error.
Goof (miscellaneous): When Dilbert, Wally, and Alice find the hiding place of the little people and are watching their party, one little person has no head.
Goof (anachronisms): The program for the old computer is said to be written in COBOL, but what's shown on the screen is in C++, a language developed much later.
Goof (revealing mistake): When we see the computer screen reflected in Wally's glasses, the program is still readable left-to-right, instead of reversed.
Goof (factual errors): Dilbert states that "a big round number is coming up" and the episode is entitled Y2K, suggesting the new year's eve would be followed by January 1st, 2000. The real start of the third millennium and the 21st century starts on January 1st, 2001 and NOT 2000 as suggested in popular culture. As an engineer he should know that.
Goof (factual errors): While looking at his perpetual calendar, Dilbert asks Dogbert to guess what day of the week January 1, 2222 will be. When Dogbert replies "Twos-day" (i.e. Tuesday) Dilbert replies in the negative. January 1, 2222 will, in fact, be a Tuesday.
Goof (errors made by characters, possibly deliberate errors by the filmmakers): While checking his perpetual calendar, Dilbert informs Dogbert that June 30, 2014 will be a Thursday. That is incorrect; it will be a Monday. Moments later, Dilbert asks Dogbert to guess what day of the week the first day of the year 2222 will be; Dogbert guesses "TUE-sday?" Dilbert responds "No, but that would have been good, too." Actually, January 1, 2222 WILL fall on a Tuesday.