Whenever Jazz is thrown out of the house, he is wearing dark glasses, even if he entered the house in clear glasses. The footage of Jazz being thrown out was done many times on the same day, so the directors could make sure he was wearing the same shirt in episodes where he was thrown out but must have forgot about the glasses.
The living room changes, and a set of stairs appears.
The opening credits feature Will & Jazz playing basketball together back in Philly. This contradicts the Series second episode where Will meets Jazz & hired him as Ashley's music tutor.
Whenever Queen Elizabeth is mentioned, Geoffrey refers to her as "Queen Elizabeth". British subjects address the Monarch as "His Majesty" or "Her Majesty", so Geoffrey would say "Her Majesty Queen Elizabeth".
Will and Carlton are supposed to be 15 or 16 when the show starts. They go to a conservative button down prep school, but they have mustaches. Aunt Vivian and Uncle Phil are their caretakers, and they are supposed to be very strict.