Continuity mistake: When Eggsy is in the interview room at the police station, in a wide shot the tape recorder is on the table by itself, with nothing around it. Eggsy demands a phonecall, the police officer leaves, and Eggsy then reaches beside the recorder and picks up a cordless phone which has appeared from nowhere. (00:16:45)
Continuity mistake: In the end credits scene, when Eggsy appears in the pub, Dean is holding a pint glass in his hand, but in the next shot, the glass is suddenly on the table.
Answer: Details aren't given, but it seems that Dean is involved in local crime along with the gang that hangs around with him. Even if Harry is bluffing, and doesn't have specific proof, it is clear that he is abusive and he has the recording of him threatening Eggsy.