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He played Billy Bob when he had an obvious concussion, then berated him for passing out on the field due to the injury, and to such an extent that Billy Bob was nearly Driven to Suicide.
Mox is brought up to starting QB because the previous one sustained a horrific knee injury, requiring surgery. How was this Kilmer's fault? Well, Lance's knee was shot to hell, having layers of (untreated!) scar tissue due to Kilmer talking him into taking some painkillers rather than sit him out, and keeping the injury secret so that he wouldn't lose a star player. So by the time the final knee injury happened, it came in the form of a Career-Ending Injury, costing Lance a scholarship and a future.
And the event that sparked the team's revolt at the end of the movie and forced Kilmer's resignation - the black running back that Kilmer didn't want to play to begin with, after proving himself in a few games, got a similar injury to Lance's. Kilmer, knowing full well what such treatment had done to the other player, tried to do the exact same thing.