it's a good idea to make sure that $FILE_NAME does not contain any special characters such as | > < because it's a potential vulnerability, especially if you get your file name from some other place like arguments

Yes, this is true - if you're using the two-argument instead of three-argument open. You said you're using Perl 5.8, where the latter is available. This is another reason that the more modern three-argument open and lexical filehandles are recommended. Also, I think that silently deleting characters or chopping off the filename at these characters, which will result in attempting to open a completely different file, is unexpected behavior - IMO it's much better to simply throw an error and refuse to open such a file and let the user figure it out, instead of taking some action that isn't what the user asked for.

open FILEHANDLE, "< *.*" so again those special characters should not appear in that space

No, as I said, '*.*' is a valid filename - strange and unusual, but valid. And again, why silently try to open a file named '.' instead?