The rooftop view from Tommy's apartment is looking southwest to downtown Los Angeles (indicating a view from Echo Park) when seen at night. Later in the film when Tommy is on his roof during the day, the background is looking southeast over Hollywood (indicating that his apartment is now located near Runyon Canyon).
In the early part of the movie, while Tommy and Greg are still in San Francisco, they proceed to a cafe to perform a bit of a live reading of a play. The cafe location (in real life) is not in S.F., it's in L.A., a place called Astro Family Restaurant, located at the corner of Glendale Blvd. and Fletcher Drive. The same cafe is shown a few minutes later when the guys are seen getting a pizza prior to departing for L.A.
At the end of the film, text states that to this day nobody knows how old Wiseau is, where he is from or how he made so much money. In actuality, his naturalization records can be found online that show he was born in Poland on October 3, 1955 and became a naturalized U.S. citizen in 1984 in San Francisco. According to Sestero, he moved to France before immigrating to the United States and changing his name to Thomas Pierre Wiseau (likely from Tomasz Piotr Wieczorkiewicz or Wieczór). Furthermore, a documentary filmmaker discovered he was born in Poznan, Poland. However, it remains a mystery as Wiseau will not confirm these details, and how he became so wealthy is still not known.
During the film's premiere, scenes from The Room are shown out of order. Specifically, the "You are tearing me apart, Lisa!" scene is shown before the rooftop "I did not" scene, when in actuality it is the other way around.
In the movie, Sandy shows up at the premiere. In real life, Sandy did not come to the premiere as Tommy had not invited him due to incidents on set; to boot, actor Kyle Vogt didn't even come to the premiere for similar reasons.
The scene in which a star-struck Tommy approaches Judd Apatow in a restaurant takes place in 2002, when it is highly unlikely that Tommy would have recognized him. Apatow had produced the shows Freaks & Geeks (2000) and Undeclared (2001), but did not achieve celebrity status until he directed The 40 Year-Old Virgin (2005) and Knocked Up (2007). However, as Apatow is never identified by name, it could be argued he's playing a fictional producer and not himself, especially as he's much nastier than the real Apatow.
In The Room (2003), there is a character of Peter, the glasses-wearing psychiatrist friend, who falls down while playing football, suddenly disappears and a new character named Steven appears in the movie; he came with no introduction and speaking lines that would logically have made sense with Peter. However, the "Disaster Artist" film makes no mention of this and seemingly implies that Peter (played here by Nathan Fielder) was present for the entire film.