I found the problem.
You dispatch the form through the_content filter, where you display the result instead of the regular content. Unfortunately, I display excerpts of some special posts (currently 6 of them) in my sidebar, so the hook hijacks them too rewriting their content, resulting in the total of 7 mails sent.
I recommend to sanitize the spamshield_contact_form function call (within the SpamShield plugin) with in_the_loop check (I had no idea is_main_query will not work here, view this). This helped me.
Unfortunately, I don’t use JetPack. It appears the problem is with my theme (disabling plugins did not help, but switching to twentyfourteen did).
I need to stay with the theme. Can you provide some pointers, where the problem could be? (some critical hooks/filters, or dangerous programming practices with respect to the problem) It is a purchased theme, but I have rewritten some portions of it.