Just one little efficiency pointer -- you can perform the substitution and check if the file ends in .mp3 with one s/// call:

#!/usr/bin/perl -w
use strict;

use File::Find;
find(\&process, '/Users/Shared/Music');

sub process {
    my $song = $File::Find::name;
    my $orig = $song;
    if ($orig =~ s/ 1\.mp3$/.mp3/ && -e $orig) {
      ...
    }
}
[download]