It's true, email on the droid is broken for many people. I have no experience with the Verizon email app and suggest that you see if you can use K9. You'd need all of the login data from verizon.
However, that wouldn't necessarily solve your problem. I started with the stock "Email" app. It has a few bugs, one of which is that it randomly stops polling pop3 accounts. So, I switched to K9 which has greater functionality...and the same stop polling bug. So anyway, I check out the stock gmail client and it works except that, guess what, it stops syncing with google's servers! The email apps, the OS, the firmware--something was garbage. What should have been completely automated would just quit and then require user intervention.
To temporarily fix the stock app and K9, I would manually refresh or just reboot. The gmail app would require me to go to phone settings > applications > manage applications > menu > filter > all and delete the gmail storage data. You might want to try this on your Verizon email app.
All temporary fixes until I came across 1 or 2 people suggesting a permanent fix:
DON'T USE WIFI :icon_eek:
And it's worked flawlessly for me for over 3 and a half weeks. Shut off wifi, reboot, and see if your email client works properly. Hopefully 2.1 will fix this. No guarantees but works for me! :icon_ banana:
Don't use an automated task killer or antivirus.