While the MESS driver is really very nice thanks to all the great work etabeta has done on it since you've been away, it still needs a PPU rewrite to fix graphical glitches in many games. That's the only major thing holding it back as far as I know. I'd recommend Nestopia at least for now. See here
Regarding saving - make sure you *exit* the emulated instance of the game before checking the save file. For some reason MESS doesn't actually save games when the original system saved them, unlike Nestopia and others. Save data stays in RAM while running and is committed to disk on exit. Just hope your instance doesn't crash!