1) You need to escape the the "/" within the regular expression since it's used to delimit the expression itself.
2) [[:alnum:]+] is not the same thing as [[:alnum:]]+
The former matches one character, an alphanumeric or a plus sign; the latter matches 1 or more alphanumerics.
It is required according to the posix standard. I strongly suggest that you do not depend on your implementation's behavior. Perhaps your awk allows that, but when run on a different implementation it may choke thusly:
$ echo "./comparecdna.summary" | awk '/^[.][/]compare[[:alnum:]]+[.]summary$/'
awk: nonterminated character class ^[.][
source line number 1
context is
>>> /^[.][/ <<<
AWK thinks it's an unterminated class because the regular expression delimiter is encountered.
For more info, read the "Regular Expressions" section @ awk