chdir("/")||die "Error:$!\n";
opendir(ROOT_DIR,"/")|| die "Error:$!\n";

search_dir("/","/");

sub search_dir{
     my ($dir,$fullpath) = @_;
foreach $dir_cont (sort readdir($dir)){
  next if $dir_cont =~s/^\.\.?$/;
  if (-f $dir_cont){
    log_sbit($full_path . $dir_cont) if (-u $dir_cont || -g $dir_cont)
+;
  }
  elsif (-d $dir_cont && opendir(SUB_DIR,"$dir_cont"){
    my $new_full_path = $full_path . $dir_cont;
    search_dir($dir_cont,$new_full_path);
  }
}
[download]

This code is untested. I just added the $full_path so you could keep track of the full path and I put it all into a sub. So far you have the right idea. You just need to put your logic in a routine you can call over and over again. Once you get it right, check out File::Find.