When Doug Judy is being choked in the room, the man in the mask's arm and face appear to be black, but the man Judy tells them to arrest is white.
Doug's explanation of international waters is a popular Hollywood misunderstanding. In reality, crafts in international waters still have to obey the laws of the country they are registered in.
Captain Holt wears his Commendation breast bar above his World Trade Center Breast Bar. When the WTC bar is worn, it is worn above all other medals, but below the American Flag bar.
It would make zero practical sense to have a cruise ship catering to American clientele registered in the landlocked Uzbekistan due to possible port entry restrictions.
When Amy asks Jake to grow a mustache, Jake states that he is physically incapable of growing any facial hair. However, in the first few episodes of season 5, Jake is seen with a beard.