I suspect a few things could be occuring but need more info to narrow down the cause...
1) Did you migrate the queues from OLD server to NEW server using tools?
2) Are the clients connecting via Point and Print or direct IP to the networked printer?
3) Are the clients using point and print connecting printers on the OLD server and NEW server as they access different printers? If yes, does the OLD server have a different version UPD than the NEW server?
4) Have you had HP UPD v5.2.x in this setup and upgraded from that version to a newer HP UPD version?
In the UPD Sys Admin Guide is a section on "Best practices-Upgrade" that is worth a read and will explain reasons for my questions above. For question #3, see "Versioning of print driver shared files".
If you want a quick test, here are some steps:
Install the most current UPD from www.hp.com/go/upd (today that is v5.8). During install choose the version specific driver name, not the generic "HP Universal Printing [PDL]" name. This will create a new printer object and not a printer created from migrated settings or upgraded printer event. Share the new printer object and tell one of your users that is reporting issues to start using that printer (they too should create a new printer object-- do not have the open the ADVANCE tab of an existing printer and simply change the driver-- that would be a driver upgrade/settings migration event).