Validation error on term-reference field when ajax'd option is submitted?
Drupal checks the integrity of the form to make sure submitted values match up with the available options when the form was built; it's a security feature. Manipulating the form on the client-side, without informing the backend that something has changed, causes the integrity check to fail.

Rather than work around it (which is possible but messy), I'd recommend using the AJAX functionality already built into the form API.

The AJAX Forms in Drupal 7 page, FAPI AJAX reference and the AJAX Example in the Examples module are excellent resources for learning about this.