Deliberate mistake: In the scene where the ministers are all crammed into the train carriage if you look over Jim's shoulder there is a sign ("Notice" "In case of Fire" etc), while the headers are in English the actually paragraphs are written in gibberish.
Character mistake: In the episode where Henry has overdue library books, they are overdue by 5 years and 23 days. Both Henry and Monroe say in the episode that the fine is around $1000 (based on 10 cents per day due 5 years 23 days)... But in reality, using that calculation, the total would come to only $185, not $1000.