Factual error: One of Angel's lyrics (in "Today For You, Tomorrow For Me) refers to the movie "Thelma and Louise." Rent (the movie) is set in 1989-90. "Thelma and Louise" was released in 1991.[This was caused when they did the move from Broadway to the screen. What happened was the stage show did not specify the year. So when they adapted the stage show to the movie, they didn't check the references. Plus it just sounds cool. Added info by Todd Loewen]
Continuity mistake: At the beginning of the film, Angel enters Mark's apartment with Tom and does her (his?) dance on the furniture. Notice that the long table has crumbs all over it. Fast forward one year later when Mimi is carried up to the apartment and placed on the table. Miraculously, the same crumbs are there. After her quick recovery, the crumbs are not only gone, but the table is polished.
Continuity mistake: When Mark is editing his film at the end of the movie, there is a segment of Angel when he was singing "Today 4 U," Mark never filmed during that scene. At no point during Angel's performance does Mark pick up his camera and film Angel. We see Mark without his camera just watching Angel.