The user couldn't play files from the network share on our server, but could if they copied them to their desktop first. They had Windows XP Pro.
They also couldn't disconnect from the share... but if you mapped to the same share on the same server with a different drive letter, everything worked fine.
When opening the network drive, you'd also notice it was in the "Internet" security zone.
Turns out there's a security setting that fixed it in this case.
Start | Administrator Tools | Local Security Policy
Security Settings | Local Policies | Security Options
Network Access: Sharing and security model for local accounts
Changed from "Guest only - Local users authenticate as guest" to "Classic - Local users authenticate as themselves".
After a reboot, the folders on the share no longer showed up in the "Internet" security zone, and all was well.