Currently the only jailbreak solution for iPod Touch 3G with OS 3.1.2 is to use BlackRa1n, this Windows/Mac jailbreak tool works for iPod Touch 3G.
George Hotz has tweeted about an important issue that most people are facing. You’ll have to check if your iPod Touch 2G or 3G, 8GB model starts with MB or MC. For MC it won’t work, so you should restore it back to the old firmware. It works fine for the ones that start with MB. I guess that should answer most of the issues …