Other mistake: In the final scenes where Eggy goes to have a fight at the pub with his mother's boyfriend they are listening to Slave to Love by Bryan Ferry. The counter says 962 whilst the tape machine is playing (electronic), but the counter does not change.
Continuity mistake: When Valentine is speaking with Princess Tilde through the prison door, his position changes during the reverse shots from Tilde's perspective. On his side of the door, his left shoulder is closer to the door, but in the reverse shot, his right shoulder is closer.
Continuity mistake: After the church massacre, you can see a row of jackets hanging next to a Confederate flag. When the shot changes, the jackets disappear. Then the shot changes again, and the jackets reappear.
Continuity mistake: When Harry and Eggsy are talking about the newspaper headlines, in Harry's study, once Eggsy sits down, the desk lamp on Harry's desk rotates between shots, the main boom arm also changes angles from vertical to set on an angle.
Continuity mistake: In the pub fight, when Galahad stuns the last thug, you see Eggsy flinch and start to move back, but when the shot changes he's sitting back up perfectly still as if he hadn't moved.
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.