Here are a couple of the more common issues I've seen running Linux on the Bay Trail NUC:
The "no desktop" desktop: After installing Linux Mint you may see the Mint logo (i.e. the default background wallpaper) but no task bar or icons. This is caused by a "phantom" display. Here's how to get around it:
No audio through HDMI (many flavors of Ubuntu): This isn't specific to the NUC as it seems to be happening on lots of builds, but it's easy to get around:
Other than those minor issues Linux has been running well for me on the DN2820 kit. If I come across any more tidbits like this I'll post them.