I've never had that problem when playing FFVI on a rom. One thing to remember is that there are two different types of ZSNES out there, one for DOS and one for Windows(it lets you run ZSNES windowed). Currently I'm used ZSNES V1.17, Win Port V0.85(it's the Windows, not the DOS one) and it runs great for me.

When all else fails, always make sure that you are using the latest version of ZSNES.