A number of students have raised questions since Monday's class concerning the appropriate analysis of Problem 5. That seems a fair indication that my first presentation of the material was not so clear. So here is another effort, walking step-by-step through the basic points.
The first question you want to ask is whether the patent judges are "Officers of the United States" within the meaning of the Appointments Clause. For if they are not, the Appointments Clause is irrelevant, and there is unlikely to be any constitutional issue (absent some other sort of separation of powers problem). The standard for who constitutes an "Officer" is articulated in Freytag, among other places, and it basically provides that an officer is someone who exercises more than a trivial amount of discretion in the execution, enforcement, or application of federal law. Do the patent judges meet this standard? Almost certainly. They appear to have a decent amount of discretion, and they are applying federal law to parties in a manner that is often final.
Because the patent judges are "Officers," their appointments must conform to the prescriptions of the Appointments Clause. This means that, if they are principal (or "superior") officers, they must be appointed by the President with the advice and consent of the Senate. If they are inferior officers, they can be appointed in the same manner, or Congress can vest their appointment in the President alone, a court of law, or a head of a department.
Here, it is irrelevant whether the patent judges would be considered principal or inferior officers, as their appointment by the Director of the PTO does not fit within ANY of the permissible means for the appointment of officers of the United States. Clearly, the patent judges have not been appointed by the President alone or with the advice and consent of the Senate. The Director of the PTO is not a "court of law." (The Director does sit on the Board of Patent Appeals and Interferences, but that is only one of his responsibilities. His official position is an an undersecretary in the Department of Commerce, an executive department. Thus, although the Director might exercise some adjudicative responsibilities, his position is quite different from that of the Chief Judge of the Tax Court at issue in Freytag.) Finally, the PTO Director cannot be the head of a department. He is an undersecretary of Commerce who reports to the Secretary. Assuming arguendo that the Commerce Department is a "Department" under the Appointments Clause, the Director of the PTO cannot be the head of that department, as there is someone above him who does, in fact, head the department: the Secretary of Commerce.
Thus, the appointment of the patent judges is unconstitutional. And this is why Congress amended the statute in August 2008 to provide that the patent judges shall be henceforth appointed by the Secretary of Commerce (in consultation with the Director of the PTO).