The empty diamond with @ARGV lets (edit: not "let's") you win a few chars:
open$:,"</usr/share/dict/words";while(<$:>){...}
@ARGV="/usr/share/dict/words";while(<>){...}
Using the magic increment on a string (eg 'a'), you can have /$a/ search for the successive letters in the alphabet (also "push if" is shorter than "next unless; push"):
$a='a';$a++while/$a/;push@_,$_ if$a gt'f'
next unless/(?=.*a)(?=.*b)(?=.*c)(?=.*d)(?=.*e)(?=.*f)/i;push@_,$_
And I thought the sorting was too verbose, so I stored the matching words by length to begin with:
@ARGV="/usr/share/dict/words";while(<>){$a='a';$a++while/$a/i;push@{$_
+[length]},$_ if$a gt'f'}@_=map{$_?@$_:()}@_
open$:,"</usr/share/dict/words";while(<$:>){next unless/(?=.*a)(?=.*b)
+(?=.*c)(?=.*d)(?=.*e)(?=.*f)/i;push@_,$_}@_=sort{length$a<=>length$b}
+@_
That's 31 fewer chars than your version, not counting the extra ' in your perl code ;-)
A chomp might be needed somewhere though, adding at least 5 chars.