A man who is still struggling to emotionally detach himself from someone will often start talking about that person. You will find him searching for an opportunity to steer the discussion in that direction and start pouring his feelings out. This is a clear indication that he is still obsessed with her and has not moved on completely. You would want to avoid getting romantically involved with such a person until he has completely gotten over his feelings for his ex.
A man hung up over someone would cease to care too much about his appearance. If he was particular about taking a shower every day, remaining clean-shaved and dressing up nicely, but has stopped caring about his looks or clothes all that much in the recent past, then the person is definitely stuck in an emotional whirlpool. He may be trying to get out of it, but the emotional pull towards his ex is probably keeping him from escaping.
If you are dealing with a man who has begun to show interest in you and looking to move things between you two at a fast pace, then there is a strong chance that he is just trying to use you to get over someone. Such a man may not even take your feelings into consideration, as he will simply want to relieve himself of his feelings for the ex.
When a man is hung on someone, you will notice him reacting to certain triggers such as romantic songs, emotional scenes in movies, restaurants, etc. These triggers may be something that remind him of his ex and consequently fill him up with grief over losing/breaking up. This indeed is a sign that he is still hung up on her.