Some quotes were wrong - use warnings would have told you. And an eval was in the wrong place.

EDIT: I shouldn't have posted this in a hurry. Sorry, this does not work.

At least for the given example this works:

#!/usr/bin/perl

use strict;
use warnings;

#FROM DATABASE TEXT
my $line = "Her house is on 34th Mt. Whitney St. near St. Mt. Helens S
+t.";

#FROM INCOMING FORM INPUTS
my $query = '(St\.\s)(Mt\.\s)(?=Helens)';
my $substitution = 'Mount ${1}';    # USER MAY HAVE ENTERED "$1"

#FOR RETURNED HTML HIGHLIGHT OF CHANGES
my $start = q|<span class="highlight">|;
my $end = "</span>";

return "Regex containing code disallowed." if $query =~ m[\(\?\??\{];
return "Regex containing code disallowed." if $substitution =~ m[\(\?\
+??\{];


my $replace = sub {
  my $evaluate = sub {
      return eval($1);
  };
    my $val = $substitution;
    $val =~ s/(\$\{\d+\})/$evaluate->()/eg;
    $val = "$start$val$end";
    return $val;
};

    eval "\$line =~ s/\$query/$replace->()/eg";

#EXPECTED TEXT AFTER SUBSTITUTION
$line = "Her house is on 34th Mt. Whitney St. near Mount St. Helens St
+.";
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