Updated to WordPress 3.9, no issues.
I finally got around to trying to upgrade to the latest kernel. I spent two days working on 3.13.1 and finally gave up. The only issue I ran into was with my nvidia driver (I was using the latest), which wouldn’t work with this kernel, due to a variety of errors. I was able to fix a few errors with patches to the driver, but it was just becoming too big a waste of time.
I decided to go back to the 3.10.x series, which some distributions have chosen as their long-term maintenance kernel. That’s usually a good sign of stability/maturity, and it was still a significant upgrade from 3.7, which is what I was running. I didn’t have any issues upgrading to this version. So far I haven’t noticed any significant improvements or regressions, and there weren’t really any new features that I use on my home machine.