Continuity mistake: When Mike is in Ed's office he is sitting in a chair he has a remote in his hand. His hand is up by his ear the shot changes, his hand is now in front of him. The remote is in his left-hand then switches to his right. When he leaves it is back in his left.
Deliberate mistake: When Tim Taylor is telling Mike about his show "Tool Time," he mentions that it lasted for 8 years. Later in the episode when Mike is asking Tim why he stopped doing the show, Tim says it's because he found it challenging to keep the show great and not run out of ideas. Firstly, while Home Improvement ran for 8 years, the show within the show of "Tool Time" was already a couple years old when Home Improvement started, as evidenced by the fact that its season 3 episode "Fifth Anniversary" was about "Tool Time" celebrating its 5th anniversary, as the title suggests. Additionally, Tim didn't quit "Tool Time" for the reasons he stated here. He spontaneously quit over creative differences with Binford's new president, who was turning the show into a sensationalist Jerry Springer type of format, and because his wife Jill had just been given a job in Indiana, and he decided the family would move there to support her.