One of the best cures for slow regexes is to improve your understanding of how regexes work. I suggest perlretut
as a starter and "Mastering Regular Expressions" published by O'Reilly.
A common problem causing exponential blowup of execution time is nested quantifiers:
There are an exponential number of ways to split up a string of a's into inner and outer quantifier bits, and if the string to match has stuff past that string of a's that can't match, it will try every possibility in the effort to match. Hence the blowup. The solution is to rewrite your regexes to not have nested quantifiers.
Update: There does exist a directive for debugging regexes (see use re 'debug' in perlretut), but it won't make sense until you have a good understanding of how regexes work.