I'm more thinking about negative character classes, which you can't do properly on UTF8. Unless all the characters you want to not match are ASCII, a special case in which the character class will still work.
The best single example is probably the regexp ".", which on real strings means "a character", but on a UTF8 string becomes something like "some number of bits of a character". The UTF8 counterpart for "." isn't nearly as readable and regexps can be complicated enough even before trying to apply them to some encoded string.
Anyway, working with UTF8 encoded data is a leaky abstraction (basic assumptions about how operations work don't hold) which requires a higher level of understanding of which operations work as they would on proper strings, and it's a plentiful source of breakage and bugs better avoided, unless you have written a UTF8 {en|de}coder yourself on some occasion and know the pitfalls by heart.