I've seen that same glitch in my personal (non-GMail) account that's setup through the EMail app.
If you delete the account and recreate it, everything will be good again, if only for a short while...
There's really no way to -just- clear the EMail app cache without wiping everything via Manage Applications, which removes -everything- in one shot. Not just your cache but your accounts and all of your settings too. Go figure.
As an alternative, K-9 in the Market is a really nice EMail app...
It's a known issue with the Droid. Are you using 2.1 and the stock messaging app? Handcent is a good 3rd party messaging app and you can use SMS Backup & Restore to backup your messages nightly. Doesn't backup mms though.