You indicate:

# similar untainting for all other user input here, then...
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and:

        print MAIL "Subject: $subject\n\n";
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so it's not clear what kind of checks you're doing on the subject. Depending on those checks, this script may be an open mail relay or not. For example, suppose the subject is set to:

$subject = "Nice subject\nBcc: john@doe.com, jane@doe.com... ";
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the mail you send becomes in fact:

From: $name
To: $sendto
Subject: Nice subject
Bcc: john@doe.com, jane@doe.com...

Message: $message
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and you've just become a spammer.

So, make sure you filter newlines from $subject as well!

Liz