I imagine the big problem is anything depending on user input, which is unpredictable. Then the unpredictability probably propagates a long way through the program.

A simple example would be something like `x = (isUserOnMars() ? "foo" : 1)`. The type of `x` depends on if the user is on Mars. In practice they never will be, but a compiler can't tell that and so must consider that case and make code appropriately generic. A JIT however can see that it always appears to be false, and optimise around `x` tending to be a number, with bailout if it's wrong (which it likely never will be). Then the use of `x` may propagate a long way through the program in all sorts of places, extending the effect.