#! usr/bin/perl
use strict;
use warnings;

my $search_term = 'Smith';

#no need to open the DATA handle, you can simply start reading it...
for my $line (<DATA>){
    print $line if $line =~ m{$search_term} ;    
}

__DATA__
Fred Smith
Jane smith
Bob Smitters
Joe Smith


__END__
This is the output I'm getting:
C:\Temp>perl test.pl
Fred Smith
Joe Smith

But I was expecting:
Fred Smith
Jane smith
Joe Smith