The videos showed Kellett leaving a petrol station without paying, taking class A drugs and being driven in a speeding car at more than 140mph.
The clips also show other people setting off fireworks in a wheelie bin and in a microwave oven in the road.
"Kellett must be in the running to be Leeds' dumbest criminal. He has handed us the evidence against him on a plate," said Leeds City councillor Les Carter.
"In the past three years, we have seen a 32 per cent reduction in crime in Leeds. If more criminals were as obliging, the city would be even safer."
Under the terms of the ASBO, Kellett has been banned from posting any image or description of unlawful activity on the internet.
Participating in, or encouraging others to participate in, the driving of vehicles in a dangerous or anti-social fashion would also break the terms of the ASBO.
Any breach of the interim order, which will last until a hearing next month, could result in a jail term.
Kellett is appealing against the ASBO, claiming that it potentially breaches his human rights by restricting his right to free expression.