Yeah, you can move to Snes9x instead if you want - that's what I use. If that can find the save game data (stored in a .srm file in the same folder as the ROM normally) and you've not been using the savestate feature of zsnes, then you should be able to continue where you left off. I'm not so certain if Snes9x can read zsnes's savestates though, but the .srm should be readable regardless of which emulator you're using.
This glitch is definitely due to an emulator being configured wrong though and not the ROM, I've seen this happen before with many games.