|| does not form a list of operands to pass to another operator. There's isn't such an operator in Perl5 (but I bet there is in Perl6). Of its two operands, it returns the first one that is true.

What you want is

if (  $FORM{'Comments'} =~ m/http|html|a href/i
   || $FORM{'addr'}     =~ m/http|html|a href/i
   || $FORM{'name'}     =~ m/http|html|a href/i
)
[download]

You can remove the redundancy with a loop

for (@FORM{qw( Comments addr name )}) {
   if (m/http|html|a href/i) {
      html_message();
      last;
   }
)
[download]

Is there a reason you didn't apply my suggestion to change
/http|html|HTML|A HREF|a href/i
to the simpler and equivalent
/http|html|a href/i
That's what the "i" does.