Are there compatibility problems with any EF lenses made by Canon?

Basically, no. Any Canon EF-mount lens will work with any Canon EOS camera (Digital and Film).

Now, there are minor compatibility issues with IS lenses on certain old EOS cameras - the lenses work, but IS control is a bit weird or the image may shake in the viewfinder. Luckily this latter does not affect image quality of the photos at all. And autofocus-only EF lenses (a handful were made) are not much use on the oddball EF-M camera, which was an EOS camera which lacked autofocus circuitry and which can only be used with manual-focus-capable lenses. But these are minor issues on the whole.

Note that this compatibility issue is only slightly complicated by the introduction of EF-S lenses, in that an EF-S lens is not an EF lens. EF-S lenses, marked with small white squares rather than raised red dots, can only fit EF-S bodies.