Well, here's a little bit of golf right off the bat. Since we are checking the input, we can get away with an eval without fear:

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

my @stack = ();
my %ops = ( '+' => \&calc, '-' => \&calc, 
            '*' => \&calc, '/' => \&calc, 
            'p' => sub { print $_, "\n" foreach @stack; },
            'q' => sub { exit 0; }
          );      

while(<>) {
  chomp;  
  if (exists $ops{$_}) {
    $ops{$_}->($_);
  # The badass regex is out of the Perl Cookbook, page 44
  } elsif ($_ =~ /^([+-]?)(?=\d|\.\d)\d*(\.\d*)?([Ee]([+-]?\d+))?$/) {
    push @stack, $_;
  } else {
    warn "Bad input: $_\n";
  }
}

sub calc {
  my $op = shift;
  my $rhs = pop @stack; 
  my $lhs = pop @stack; 
  if ((! defined $lhs) || (! defined $rhs)) {
    warn "Not enough values on stack!\n";
    push @stack, $rhs if defined $rhs;
    return undef;
  }
  my $res = eval $lhs.$op.$rhs;
  print "$res\n";
  push @stack, $res;
}
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Fix: I had the rhs and lhs backwards in the eval originally