On a 3rd gen iPad here and by far my biggest issue has been that multiple background downloads (a batch of app updates or track downloads from the store for example) will more often than not cause the whole device to deadlock, with the only way to recover being to do the power + home button hard-reboot combo.

Really hoping this was fixed in 7.1, which I'm running now and so far seems smoother (doesn't stutter anymore when switching to the task switcher view, for example).

The other persistently anooying bug I've seen has to do with text fields on some webpages (eg Outlook Web Access and the Amazon Kindle web app) where if you tap to change the cursor position inside the field, you can no longer type characters in it and have to deselect the field (by tapping another on the same page) and then reselecting it again. Makes fields on many pages simply un-editable (the Amazon web app is the worst as you have to leave the store section entirely and it breakd the product Search field). Not sure if it's page or Webkit specific but it'a been around unfixed even on iOS 6 if I remember right. Fingers crossed on that one :)