Print out the full name of the .md5 file before you try to open it:

my $checksum_file = "$file.md5";
print "Looking for existing checksum file '$checksum_file'\n";
if( -f $checksum_file ) {
    print "It does seem to exist\n";
} else {
    print "It does not seem to exist\n";
};
print "Opening '$checksum_file'";
if( ! open my $fh2, '<', $checksum_file ) {
    print "Skipping '$checksum_file': $!";
    next
};
...
[download]

That should give you a hint of the reason why open fails.