Continuity mistake: In the scene where Howard supposedly has radio sex with that blonde woman, it flashes to other locations where people are listening, including one with police officers standing by what are clearly early to middle 1990s Ford Crown Victorias. Howard did the stint in the mid 1980s.
Factual error: During Howard's "Thank You" speech to New York he gives NYC the gift of a live performance by AC/DC. The year was 1985. As the band takes the stage and launches into "You Shook Me All Night" we see Phil Rudd on drums. Rudd had quit AC/DC two years earlier and was replaced by Simon Wright. (Rudd returned in 1994, hence being part of the band when the scene was filmed).
Continuity mistake: When Howard hits Kenny with the phone Kenny's nose is bleeding. It cuts to Howard and then back to Kenny and the blood has disappeared.
Factual error: In the scene where Howard arrives at WNBC, his moustache is gone and his hair is long. The first few years at WNBC, he still had short hair and the moustache. Also his original air shift was from 4PM-8PM, later changed to 3PM-7PM to accommodate for the Knicks and Rangers broadcasts.
Continuity mistake: When Howard is young and watching the guy break the records, there is a blue coffee cup on the desk. The cup moves from under the microphone to its right. Then it disappears in one shot, but in the next shot he picks it up and throws it. Then after Howard's dad gives the speech to get back on the air, the cup is back under the microphone.
Factual error: In the scene where Howard is saying goodbye to Fred in Hartford, a Discover Card logo appears on the storefront behind Howard. This scene is meant to take place in April of 1980, but Discover Card wasn't introduced until 1985.
Factual error: In the early 80s, Howard attends the premiere of "Die Watching," a film that was not made until the early 90s.