The extractor has to hold the case in position for the firing pin to strike the primer. That puts extra stress on the extractor, and in some cases the extractor may not be up to the task. That issue can cause misfires and some possibility of an extractor failure.
You can also get the typical carbon ring buildup which may cause malfunctions when you go back to the proper caliber.
A much more dangerous (though admittedly less likely) situation can arise if the sharp edge of the chamber (where the chamber transitions to rifling) shaves off bullet material. In a revolver, there is a smooth taper in front of the case mouth so that this doesn't happen, that's why it's safe to shoot shorter cartridges in a revolver. In an autopistol, there's typically a sharp lip in front of the cartridge mouth which the front of the case bears against to establish headspace. If you're shooting the right length cartridges in the chamber, the bullet never touches that lip, but if you shoot shorter cartridges in the chamber, small amounts of bullet material can be shaved off at each shot and build up at the front of the chamber. Eventually that material could build up enough to cause a bore obstruction.