Well, after a few days with this update, I'm beginning to notice a couple of issues.
The first one is multitasking. Most of the time, multitasking between apps is fine and dandy, but what I noticed is that if you have multiple tabs open in Chrome, switching between it and another app can cause reloads. I was switching between Chrome (with only 2 tabs open) and Google Docs the other day, and half of the time when I would go back to Chrome, the tabs would reload themselves. It hasn't happened with one tab opened, however. Maybe this was happening before the update and I just noticed this, or it's something Lollipop did, I'm unsure.
But the second issue is, you may remember the touch screen bug from KitKat (where the screen would stop registering at certain times and you had to turn the screen off and on to fix it). Guess what, it's still there in Lollipop, although the good thing is that it's slower to stop registering, and the bug doesn't happen as often as it did before. It's kind of annoying that they didn't pick up that bug, but at least it improved somewhat.