Ugh, really hoping they just ignore TT.
It would be easy to give Tim logical weaknesses without bringing up that dreck, and a Tim who feels insecure about not being "The Leader" is an out of character Tim IMO.
For me, Tim's biggest weakness is lack of trust. He's the type who would screw up to protect stephanie, or underestimate Cass's ability to handle a non combat situation, or make a mistake because in a sensitive situation he has one eye on the mission and one eye on clayface.
He also seems like the type of person who would spend too much time trying to come up with the best solution when time may only allow for an okay solution.