Character mistake: Stabler calls for an LPR check on a vehicle. The description of the vehicle he gives is for white Mazda Sentra. Mazda doesn't make a Sentra. Nissan makes the Sentra. (00:09:45)
Character mistake: The ship's doctor is sometimes addressed as "lieutenant surgeon" instead of the correct "surgeon lieutenant."
Character mistake: Bucky says he read The Hobbit in 1937 when it first came out. But in 1937 he was still living in New York, and The Hobbit was only available in the UK at that time, with fairly limited numbers printed. It wasn't available in America until 1938.
Character mistake: Captain is warning German travelers about poison oak and ivy, but holding up the leaf of an oak tree.
The M.O.D.O.K. That Time Forgot! - S1-E2
Character mistake: M.O.D.O.K. refers to Hoobastank as "the Beatles of the late 90's." Hoobastank only released one album in the 90's, and they didn't become popular until after they released their second album in 2001.
Character mistake: A police officer describes a murder weapon as a revolver. It is an automatic pistol.
Episode #1.3 - S1-E3
Character mistake: Richie Gulliver is referred to as Rory Gulliver on the newspaper headline. As he's supposedly a very well-known Member of the Scottish Parliament, it's unlikely a newspaper would make a mistake like this.