In the episode, "Moving Targets" Hiyono and Rio are held hostage in a hotel and are tied to chairs. In this episode, Hiyono isn't wearing her coat but in the following episode she is.
In the episode "Whispering Shadows", The injury the Hunter receives switches from his left arm to his right arm for a moment before going back to his left for the rest of the episode.
In "Only One Wise Action" Rio drops Ayumu's watch and the watch band lands twisted, but the next time we see it the watch band is flat.
In "Goodnight Sweetheart" We see a close-up of Kousuke's feet as he stops to question Hiyono. He is shown to have stepped off of grass onto dirt, but a few seconds later we see he is in the middle of the street with no grass around.
In the English dub, Kousuke's birthday was given as August 28, 1987 and his age is stated to be 17. Although the anime was originally broadcast in 2002, no chronological year was stated in the series. So, it's possible that the anime was set in 2004-2005, when Kousuke was 17.
When Hiyono drops the bombs disarm key from train it falls straight down. However because the train was moving forward the key would have fallen at an angle.