• Instead of using the $_ variable for the name, I would suggest using $File::Find::name because that will more likely hold the correct filename you want.
• Maybe I'm not understanding something but you're making your global changes to $buffer, but I only see it used once. Did you mean to make your change to $data?
• Since you want to loop through many files and directories, you should perhaps change your dies to warns so the script continues, and you can hand modify the files.
• Doing global changes will probably be faster if you slurp the whole file into memory all at once:
  

      {
          local $/ = undef;
          $buffer = <IN>;
      }
  [download]

• Regardless of whether or not the file contains OLDWORD, you're opening the file and rewriting it (which is where your corruption is probably coming from). You should only rewrite the file if you made any changes to it. The s/// regex returns the number of changes made, so as long as catch that change, you can test on the value later.
• And according to the mantra here, always always

  use strict;
  use warnings;
  [download]

Here's a quick untested rewrite I did to highlight the points I made.

use strict;
use warnings;

use File::Find;

my @dirs = qw( . );

find ( { wanted => \&change, no_chdir => 1}, @dirs );

sub change
{
    my $file = $File::Find::name;
    
    if ( -f $file && $file =~ /\.html$/ )
    {
        open(IN, $file) or warn "CANT OPEN FILE!\n";

        my $buffer;

        {
            local $/ = undef;
            
            $buffer = (<IN>);
        }
        
        close IN;
        
        my $changecount = ($buffer =~ s/OLDWORD/NEWWORD/gi);

        if ($changecount)
        {
            open(OPF,">$file") or warn "NOT OPENING FILE FOR MOD, $!\n
+";
            print OPF "$buffer";
            close OPF;
        }
    }
}
[download]

This could be optimized and shrunk I know, but I'll leave that to the gurus. I hope this helps.
Take care,
bcb

EDITED: Per a notice from Oaklander, the script would enter directories, but was not changing any of the files. A quick modification changed the call to File::Find from find ( \&change, @dirs ); to find ( { wanted => \&change, no_chdir => 1}, @dirs );.

I tested the code and it works as Oaklander needs.