possible IE8 problem
I have had exactly the same problem occur, but I can't confirm that it's browser specific. Had one person fill out the form, submit (no email sent, directed to thank you page as if it was sent) using both IE 8 on PC and Safari on iPad. Have tried both and cannot reproduce, but I've had several people using the form encounter this same error where (to them) it appears everything is fine but no email to me is generated.
I did just update my Contact Page script to the 1.0.3 version (errors were with 1.0.0). Hoping this fixes it but unsure that any of the 1.0.3 changes would affect this issue.