I started having this problem just a couple days ago, not sure what started it but I ended up with four threads dated 1969 that I couldn't delete. I read through various forums which suggested a number of fixes but nothing worked.
I did mange to fix it myself though, or at least it's fixed for now. I did this about an hour ago and have rx/tx about 50 SMS since then with no return of the bug.
Download SMS Backup & Restore and back up your messages if you want to keep any of them, this fix will wipe EVERYTHING from the messaging app.
From the Messaging app thread list, press Menu and select Delete Threads. It will ask you to confirm that you want to delete all threads. Say "yes" obviously and bye bye stuck threads from 1969. Of course, bye bye to all the other threads too but that's why you made a backup. From SMS B&R, restore your messages and you should get everything back, minus the 1969 threads.
Your mileage may vary on this one so try it at your own risk. Don't complain to me when you delete that thread with the hottie from the bar the other night. You know, the one with all the pictures she sent you?