You probably need to set a "From:" header (at the very least) in the additional headers parameter for mail(), and its value probably has to be a valid email address on your web host. But now we're getting into stuff a bit more complex than a plain old syntax error, and there may not be a one-size-fits all answer, depending upon how your web server is configured.
Also, since your message is HTML, you probably want the Content-Type to be "text/html", not "text/plain" -- but that should not be stopping the mail from being sent.
PS: At least for now, you should check the return value from mail() to see if it's false, and if so output or log some sort of debug message to that effect, so you know if the problem is that the mail was not sent versus mail() thinks it was sent but it never made it to you (and don't forget to check your spam folder).