It strikes me that regular expressions are not understood well by the majority of developers. It also strikes me that for a lot of problems where regular expressions are use
The most hassle I see is when people try to parse non-regular languages with regular expressions (yes, that includes all programming and many markup languages, yes, also HTML). I sometimes wish all coders had to demonstrate that they have understood at least the difference between context-free and regular languages before they are allowed to use regular expressions. Alternatively, they could get their regex license revoked when they are caught trying to parse non-regular languages with them. Yes, I'm joking, but only half.
The next problem arises when people try to do more than character matching in a regular expression, for example, checking for a valid date, perhaps even including leap year considerations (this could also lead to regex license revokation).
Regular expressions really are just a convenient shorthand for a finite state automaton (You know what that is, don't you? Where is your regex license, please?). The problems come from people expecting some kind of magic from them, not from the regular expressions themselves.