A lot of people (myself in the past included) have judged Tim's mechanics at the FT line as bad. However there are two points to consider.
First, one of the bad part of his mechanics is that Tim swings the ball from a lowered arm position to the top of his head before releasing. That long swing is bad for consistent delivery at the free throw line. The best thing to do is actually to minimise the swing by starting with the ball at higher than chest level.
But Tim has to shoot it the way he does, because that is how he shoots the ball in the field. He uses that low to high swing to get to the free throw line because guys always think they can strip the ball from him and get his arm instead (though Sheed and Ben seldom get called for it). He can't change this at the line and keep this in the field. As a nine-year veteran, he's stuck with it.
Second, Tim is unlike Shaq, another notoriously crappy free throw shooter. Shaq is just plain bad. But Tim is erratic. He can go 15/15 in one game, then 3/12 in the next. This really tells you that all the preoccupation with his mechanics is quite misplaced. His problem is, first and foremost, a mental one.
I honestly think that Pop is being too kind to Tim in trying to let him solve the problem by himself.
Whatcha gonna do when Huxamania runs wild on you?!!