While iTunes 11.0.1 appears to have fixed most of bugs reported in the application’s initial 11.0 release (including those I covered in a previous column), a few lingering issues remain.
AirPlay bug
One bug that continues to generate heat in Apple Support Communities concerns AirPlay. Numerous users find that, after updating to iTunes 11.x, content streamed to an Apple TV (or other AirPlay device) can stop playing unexpectedly. This can occur as early as the middle of the first played song or as late as an hour or more into a playlist or movie.
Evidence points to iTunes as the ultimate cause, as people report that the symptom affects any and all of their AirPlay devices. As a few users pointed out, media can stop playing if your Mac goes to sleep (duh!). However, most users note that unwanted halts occur independent of sleep.
A usually successful work-around is to go to iTunes’ AirPlay menu and shift to the Multiple, rather than Single, option (see figure below). If your AirPlay device connects via Ethernet, another potential work-around is to switch from the wired connection to a wireless one. This is reminiscent of a similar switch that remedied an inability to install the Apple TV 5.1.1 update.

On a personal note, I have had a similar problem with premature halting of playlists in iTunes 11. However, it is not restricted to AirPlay. It occurs on my Apple TV even when streaming directly from my Mac.
Hotspot bug
An iTunes-related Personal Hotspot issue dates back at least as far as iTunes 10.7. The symptom is a failure of the USB Hotspot option, when connecting an iPhone or iPad to a Mac. Unfortunately, based on reports in Apple Support Communities, the bug remains present after updating to the latest 11.0.1 version of iTunes.
The most frequently recommended work-around is to use Kext Utility to replace the currently installed AppleUSBEthernetHost.kext file (located in /System/Library/Extensions) with a prior version as obtained from the web. Precise details on how to do this can be found in another Apple Support Communities thread. One further thread implicates iPhone Configuration Utility as a co-conspirator. Postings here advise deleting the Utility (as well as its receipts file, accessed via Terminal) before removing the aforementioned kext file.
Although the fix should allow USB tethering to work again, it is not an ideal solution. First, the next time you update iTunes and/or OS X, the replacement file may get wiped out by the newer install, with the symptom returning. Second, any custom modification to the content of the Extensions folder is risky. Older replacement files may turn out to be incompatible with other aspects of the current OS, resulting in unpredictable problems separate from whatever you are trying to fix. However, until Apple addresses the ultimate cause, kext replacement may be worth a try. Just make certain you have backup copies of any removed files, in case you need to do a restore.