Your code is basically

foreach my $file (@files){
   ...
   mkdir(...) or die("...");
   move(...)  or die("...");
   ...
}
[download]

So change it to

foreach my $file (@files){
   ...
   mkdir(...) or do { warn("..."); next };
   move(...)  or do { warn("..."); next };
   ...
}
[download]

or

foreach my $file (@files){
   if (!eval {
      ...
      mkdir(...) or die("...");
      move(...)  or die("...");
      ...
      1;
   }) {
      die("Error processing file $file: $@");
   }
}
[download]

Update: Better yet, use a sub!

sub process_file {
   my ($file) = @_;
   ...
   mkdir(...) or die("...");
   move(...)  or die("...");
   ...
}

foreach my $file (@files){
   if (!eval { process_file($file); 1 }) {
      die("Error processing file $file: $@");
   }
}
[download]