Most common issues with tape devices:
1) Tape drive asks for cleaning more frequently.
2) Media will be marked as full after writing very less amount of data to it. (Will happen with all the media in the library)
3) Media requested by BE may not be inserted properly into the drive.
The first two indicates that there is a problem with tape drive. Investigation has to be done with tools provided by the vendor. Like HPLTT tools for HP drives, IBM ITDT tool for IBM make etc... Perform a write test also along with the general investigations. And some times the drive temperature also create problems. (Drive fan assembly may be having issues). If any problems reported during the testing by using vendor tools, contact the vendor and ask for a replacement.
The third indicates there may be a problem with robot. In this case you can see something like "Stow operation failed at slot XX" and "Filed to stow at Drive n" (In case of Tandberg libraries). And the only way to take the media out from drive will be either rebooting the library or b physically removing the drive. If you remove the drive you can see the media inserted half-way inside the drive.In this case we can test the functionality of robot by performing cycle test.