local $SIG{__DIE__} = sub {
  my ($d) = ( $_[0] =~ /line (\d+)\.$/ );
  unless ($d) {
    print STDERR $_[0];
    return;
  }
  
  my $context = 3; #number of context lines
  
  seek DATA,0,0;
  while(<DATA>) {
    next if $. < ($d-$context);  #cycle until context starts
    
    warn ($. == $d ? '>' : ' ')  #mark line if it contains the error
         .sprintf('%4d ',$.)     #use 4-place line numbers (alignment)
         .$_;                    #show code on line
         
    last if $. > ($d+$context);  #move on once we've finished context
  }
};
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The actual run-time efficiency on long code will be helped by the last if.. line: there's no reason to keep doing I/O once your context has been exhausted.

The other modifications are largely maintenance-minded:

1. variable for number of context lines makes it easier to change your mind about context later;
2. using the (?:) syntax allows me to have all formatting done in one place, making it easier to change the format of printed lines at will;

I also fixed one potential bug in your regex: you would have matched any 'line \d+' in the string -- I could break your code by die('I had a problem reading the data file at line 12'). You'd see the context of your code around line 12, but the relevant code might be around line 60 or something. The new regex takes the match at the end of the message.