Now that martin has solved your basic problem, I'd just like to point out short your code could be: 
my $path = "./mail";
my $bkup = "./backup";

open MAILDIR, $path;

for my $mbox ( grep { -f "$path/$_" and -s _ } readdir MAILDIR )
{
    rename "$path/$mbox", "$bkup/$mbox";
    system( "perl -ne 'print if /^From/..-1' $bkup/$mbox > $path/$mbox
+" );
}

[download]
(That assumes that the backup directory is not on a distinct disk volume.)

update: as capoeiraolly points out below, that version backs up all mailbox files, not just the ones that need fixing. To avoid that, just add a few lines at the top of the for loop: 

for my $mbox ( grep { -f "$path/$_" and -s _ } readdir MAILDIR )
{
    my $first = do { open M, "$path/$_"; <M> };
    close M;
    next if ( $first =~ /^From / );

    # ... do rename and system calls on bad files only
    rename "$path/$mbox", "$bkup/$mbox";
    system( "perl -ne 'print if /^From/..-1' $bkup/$mbox > $path/$mbox
+" );
}

[download]

In reply to Re: Strange problem trying to clean garbage from start of mailbox file by graff
in thread Strange problem trying to clean garbage from start of mailbox file by capoeiraolly

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