Hello!
Thanks for the help, I found the cause of the error. The mail was incomplete because it had no sender. I am using the PHPMailer plugin, which was filled out, but in the Name and Email line in the general tab, only the name was given. I thought I shouldn't have to enter the email address separately there if it was set up in the plugin. I was mistaken, although it is clearly written: This email name and address will be used as the From address for all mails sent by Zenphoto. When filled in, it works like a dream.
Thanks again for your help!