I have a lot of problems with Day of the Tentacle as well, but if I save (very) often I can progress into the game. If I continue from a save point, I can go further ... and so on, I haven't found any specific points where the game fails (yet)

I don't know if it is a CPU (spikes) or RAM (bleeding) issue, but it sounds like either. I haven't checked out 1.1.0pre, as I will wait for the final release. Keep it up