The 22-year-old defender appeared in Edinburgh Sheriff Court yesterday and admitted two charges of breach of the peace which happened as the Tynecastle side celebrated the end of the season on 25 May this year.
Fiscal Depute, Caroline Kubala, told Sheriff Elizabeth Jarvie QC the player had been turned away from the Lava and Ignite nightclub in Tollcross.
He later shouted abuse at one of the staff and after the police were called was taken to St Leonard's, where he became "volatile" and threatened officers, saying: "I will remember all of your faces".
Wallace was originally charged with threatening to shoot the door staff and it was this report that led to the police following and arresting him, the court heard.
After spending the rest of the morning in the cells, Wallace appeared in the sheriff court and pleaded not guilty to the charges. His guilty plea followed the deletion of the accusation that he threatened to shoot the staff at the nightclub.
Defending Andrew Houston said the behaviour of Wallace, of Carrick Knowe, had been "immature and ill-judged".