I just updated to JB, and now when I attempt to copy text the phone reboots (with ICS the app just crashed).
EDIT: PROBLEM SOLVED
After my phone rebooted, I decided to go into S Memo and try it there. First, though, I switched to the Samsung keyboard (I use SwiftKey) and attempted to clear the clipboard using the method described by another user earlier in this thread (hold down 2nd key from the left on the bottom, then select the clipboard - then clear all). The clipboard was, in fact, full with 20 items - despite Clipboard Cleaner saying my clipboard was empty when I attempted to use it. Before JB update, attempting to clear the clipboard in this manner using the Samsung keyboard did not work - selecting the clipboard icon did nothing. Now, after JB update, I was able to see the clipboard items and clear them. Following this, I am now able to cut and copy text in various applications (including Chrome) without a problem.