For my part, I just did the update, and Swype simply would not work. I'm very familiar with the bug mentioned and switching the input method to get it to fire up again, but this time, despite repeated attempts, reboots, etc. it simply would not go and I had to completely reinstall.
The good news is that this is only the second install I have made, and it is working fine after that, but I do agree with the comments to not uninstall/reinstall unless absolutely necessary (which, in my case, it seemed to be).
I have this exact issue, it is not just the known bug:
Did you completly un-insatll the app and the installer and download all new?
How many installs does the Beta let you do?
Thanks for any answers, Man will I hate losing SWYPE...
Yes, I had to completely uninstall and reinstall, and I had lost the e-mail they had sent me, so...
1. Go to the Swype website and log into the beta site (it's closed now, so if you were not already signed up, I'm afraid you won't be able to get in. @jramey-it sounds like you were already part of the beta, so you will just need to login to My Swype.)
2. There is a link there to resend the beta e-mail, click that if you need to to get the link onto your Droid.
3. Uninstall Swype application (you don't need to worry about the installer)
4. Click the link in the Swype e-mail to download the new installer (you might be able to run the installer already on the Droid, I wanted to start completely clean, so I didn't try that).
5. The installer will prompt you for your username and password, so enter that information and login.
6. Swype will reinstall, and essentially, you set it up again.
It would not surprise me that this process will wipe out your dictionary, but it will get Swype running again. Also, be aware that the previously mentioned bug that results in having to switch input methods after a reboot is still existing here, but I have had no problems switching to the Android keyboard then back to Swype, and it works just fine.
Now, regarding how many downloads and installations you are allowed under the beta, I honestly don't know. Perhaps somebody else can jump in with that information.