I know my post is a little late...
Maybe we have a disctinction in our definition of "static parsing", but I think that no language can actually be statically unparseable as long there is a finite number of parsing rules. Under this condition, there should be a finite number of possible derivations for a certain number of generated symbols. In Kennedy's example :
whatever / 25 ; # / ; die "this dies!";
Two interpretations are possible. There should not be any problem if the compiler find the two ways and produces a check branching to the two interpretations. Something like this:
whatever / 25;
whatever (/ 25 ; # /);
die "this dies!";
When we think about it, the Perl interpreter already does this. So technicaly, parsing Perl is not a undecidable problem. You only proved that there could not be a single way to parse Perl - and yes, it is a problem for text editor's syntax-highlighting.