I would try putting $table into a Scrolled Pane, rather than a Frame. Frames don't deal with Scrolling well, but Panes do.

#!/usr/bin/perl
use strict;
use Tk;
use Tk::Pane;

my $mw = MainWindow->new;

$mw->geometry( '400x250' );

my $mwf = $mw->Scrolled(
   'Pane',
   -scrollbars => 'ose',
   -sticky     => 'nwse',
)->pack( -expand => 1, -fill => 'both' );

my $f1 = $mwf->Frame()->pack( -expand => 1, -fill => 'both' );
my $f2 = $mwf->Frame()->pack( -expand => 1, -fill => 'both' );

my %dudes;
my $dude_count = 1;

foreach my $fr($f1, $f2){
  foreach (1..6){
    $dudes{$dude_count}{'text'} = $fr->Text(
       -background => 'white',
       -foreground => 'black',
       -height     => 10,
       -width      => 22
   )->pack(-side=>'left', -expand => 1, -fill => 'both' );

   $dudes{$dude_count}{'text'}->insert('end', "\n Dude $dude_count\n")
+;

  $dude_count++;
  }
}


MainLoop();
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