If you meet all the requirements to claim your son as a dependent, you can claim him as a dependent regardless of how old he is. He could be 50 year old, but if you met all the requirements, you could still claim him as a dependent.
The 3rd chapter of Publication 17 has the general rules on who can be claimed as a dependent. P17 is free at www.irs.gov .
The full-time student requirement is an exception for the earning requirement of the dependent. In general, a person earning at or above a certain amount cannot be claimed as a dependent. However, qualifying student can still be a dependent despite earning above the amount.
He can be claimed as a dependent as long as you paid more than 50% of his support for the taxable year, whether he is a student, is working part-time or not.