You shouldn't read and write to the file at the same time; instead make a new file, then copy over:

#!/usr/bin/perl -w
use strict;
use fatal;
use File::Copy;

open( FH, "<test.txt" );
open( FH2, ">test.txt.tmp" );

while ( <FH> )
{
  s/^(\s+)//g;
  print FH2 $_;
}
close FH;
close FH2;
move("test.txt.tmp", "test.txt");
[download]

Hope this helps,,,

PS. check out perldoc perlrun to learn how to do this in one line.

update: atcroft, runrig and Zaxo: are you guys on a race or something?