My approach does split out the lines into markup/non-markup, which you said you want to avoid. I use a simple hash to remember whether it was time for an open or close tag, or no tag at all to prevent opening a tag and not closing it.

It handles nested tags (e.g., */stuff/*), but doesn't check for mis-nested tags like Tye's solution does.

Enjoy.

#!/usr/bin/perl -w
use strict;

my %sc = qw ( \\* b / em _ u );
my %counts;
my %opened;

sub track  {
    $opened{$_} = 1 - ( $opened{$_} || 0 );
    return "<$sc{$_}>" if --$counts{$_} > 0 && $opened{$_};
    return "</$sc{$_}>" if ! $opened{$_};
    $_;
}

sub reg_fix  {
    my $line=shift;
    %counts = (); %opened = ();
    $line =~ s/<([^>]*<)/\&lt;$1/g; # Replace unmatched < with &lt;
    my @elems = split '(<.*?>)', $line;
    $line =~ s/<.*?>//g;
    $counts{$_} = @{[$line =~ m/$_/g]} for keys %sc;
    for my $elem ( grep !/^</, @elems )  { $elem =~ s#$_#&track#eg for
+ keys %sc; }
    join '',@elems;
}

print reg_fix($_) for <DATA>

__DATA__
go/to <img src='http://allpoetry.com:8080/images/smile/happy.gif'> /th
+x/ <img src='http://allpoetry.com:8080/images/smile/happy.gif'> _sill
+y *to_*
Well, if < _$20_, you *need* <a href="...">this</a>
[download]

Which produces :

go<em>to <img src='http://allpoetry.com:8080/images/smile/happy.gif'> 
+</em>thx/ <img src='http://allpoetry.com:8080/images/smile/happy.gif'
+> <u>silly <b>to</u></b>
Well, if &lt; <u>$20</u>, you <b>need</b> <a href="...">this</a>
[download]

(Update - simplified code, egregious abuse of $_)