Useful, certainly, but it seems to me you're defining "unmatched braces" as a mismatch in the count over the whole document of left and right versions of the brace types. By my definition, at least, the term is stronger than that: braces must also be properly nested (i.e. '({)}' is invalid). I'd be more inclined to do something like the following (a fairly simple stack model), which catches such errors and as a bonus gives more information about where the error occurred:

#!/usr/bin/perl -w
use strict;
my %x = (')'=>'(','}'=>'{',']'=>'[');
my @braces = ();
while (<>) {
  s/\\(\(|\)|\{|\}|\[|\])//g;   # yank out escaped braces
  for (split //, $_) {   # split each line into chars
    push(@braces, $_), next if (/\(|\{|\[/);   # push if left brace
    /(\)|\}|\])/ and   # if right brace
      (@braces > 0   # and left braces on stack
       ? $braces[-1] eq $x{$1}   # and right brace matches left
         ? pop @braces   # pop the pair
         : (print("unmatched '$braces[-1]' before '$_' on line $."), e
+xit)   # saw a left without correct right
       : (print("no match for '$_' on line $."), exit)   # saw a right
+ with no stack
      );
  }
}
print "passed!\n";
[download]

This is barely tested, so nobody go using it anywhere. Granted, this doesn't take quoted braces into account, but that's a whole different story.