1-2 other things to check on the new switches - check for loops as well as pre-set the speed/duplex of the ports going to the 3300's. Sometimes they switches don't auto-detect properly and cause random issues.
This is definitely the troubleshooting path I would be thinking about - if the switchports are showing errors, and if the errors are indicative of a duplex mismatch, you should ask the network guys to change their end to auto/auto, and double-check all the Access ports that phones are on at the same time.
What can happen is that the switchports see lots of errors and occasionally reset themselves, giving you a brief outage.