I just did the update to FW 3.1.3 and used redsn0w to jailbreak. It worked fine...no problem. I did not have the unlock. If you are interested in the unlock (like blacksn0w), stay away from this. This is JB only.
Here's what I did, FYI.
BTW, I used a Mac.
1. Backed up iPhone 3G to iTunes.
2. Copied the iPhone 3.1.2 firmware from Library/iTunes to desktop
3. Downloaded iPhone firmware 3.1.3 with iTunes
4. Restored iPhone 3G with iTunes.
5. Did not set up as new phone; restored using last backup
6. Downloaded and installed redsn0w 0.9.2. Closed iTunes.
7. Ran redSn0w, pointed it to FW 3.1.2 on the desktop, installed Cydia only.
8. That's it!
Here's what I did, FYI.
BTW, I used a Mac.
1. Backed up iPhone 3G to iTunes.
2. Copied the iPhone 3.1.2 firmware from Library/iTunes to desktop
3. Downloaded iPhone firmware 3.1.3 with iTunes
4. Restored iPhone 3G with iTunes.
5. Did not set up as new phone; restored using last backup
6. Downloaded and installed redsn0w 0.9.2. Closed iTunes.
7. Ran redSn0w, pointed it to FW 3.1.2 on the desktop, installed Cydia only.
8. That's it!