Character mistake: The officers count the inmates and say there's 10 missing. There are indeed 10 inmates hiding in the pool. However, Pennsatucky and Chang had escaped the prison. The officers counted Linda as an inmate, who had been hiding in Litchfield the whole season, and wasn't on the list. That would make it 11 people missing, not 10.
The Committee on Human Rights - S5-E7
Character mistake: Renee refers to Indiana University as U of I. It should be IU. U of I would only refer to the University of Illinois, one of their main rivals. (00:31:00 - 00:33:00)
Character mistake: Several times Tommy addresses Sir Oswald Mosley as Mr Mosley instead of the correct Sir Oswald. Mosley never corrects him, which given his snobbishness portrayed throughout the series seems highly unlikely.
Character mistake: Lance and May walk into a bar in Massachusetts. As they enter, the camera pans and shows a large banner on the front window. The banner is advertising "game day" food and drinks. In very large letters the banner shows Boston Red Socks. The actual correct spelling is Boston Red Sox. (00:05:45)
Episode #1.2 - S1-E2
Character mistake: In the incident room Danny's height is written as 4ft 8inches / 112 cm. 4'8" is 142cm. (00:06:48)
Chapter 26 - S2-E13
Character mistake: Typing letter to the President on old typewriter, Frank thinks "stared at desk" but types "started at desk." (00:24:00)
Character mistake: The language peculiarity of the series refers to any wheeled vehicle as a "roller." The character "General Tak" accidentally breaks the language rules near the end of the episode and uses the word "car."