First check your governing documents and state law (which can usually be Googled). If you do not find anything, parliamentary procedure allows for a nominating committee and then for nominations from the floor. I have not heard in WA State of any reason why current Board members cannot be on a nominating committee.

In our docs it reads that at the general annual meetings that is the time where the unit owners vote for the board of administrators. Then the board of administrators picks the officers. But generally our unit owners vote for the officers directly. go figure. Then in the interim if an officer resigns or is deposed they remaining administrators can appoint an interim officer. 
I do not understand the need for a nominating committee or why someone cannot nominate themselves. But it sounds like they got lawfully elected. RYDF.

PS: Our governing documents do not call for nominating committees. The Board has two options (1) to elect Board members at the Annual meeting (2) Have a mail in ballot. Neither approach calls for or allows a nominating committee, but all Associations and state laws are different.

There will always be groups that strive for power only to run the association for their own comfort and convenience. They never care about costs, etc. because they can always recoup their own. Lesson - never vote in more than one person from a group of friends.

Our Bylaws state that "The association shall appoint ... a Nominating Committee ... ." Our association has 78 members. Our fall 2012 newsletter stated we would need candidates for the Board as the terms for two members would be ending. Thirty days prior to our annual meeting every owner received a letter announcing the meeting and restating the need for candidates, a nomination form was attached with instructions. By the time the annual meeting came around, we had zero candidates. At the annual meeting we asked those in attendance if they would like to be considered for the Board positions. You could hear crickets. The two Board members had to re-volunteer. 
 
The point I am trying to make is that even though our bylaws state the need for a Nominating Committee, we cannot even get the other owners to step up to become a member of the Board. With no candidates there was no need for a Nominating Committee. 
 
The purpose of the Nominating Committee is to validate the nominations, making sure all the information was provided probably so that a brief summary of each candidate's credentials could be presented at the annual meeting. Bottom line, a Nominating Committee is nothing more than a way to involve owners that are not on the Board. 
 
Was it wrong for your President and Vice President to be the sole members of a Nominating Committee? If your Bylaws are like ours, then yes. Was it unethical? That may be a stretch but if other owners feel the same way, call a special meeting and recall the President and Vice President. Before you do that, you may want to ask the President if they refused any nominees from the ballot. Also, it was the owners that voted for the candidates, so the President and Vice President did not just wave a wand and bam, the candidates were on the Board. In conclusion, no harm, no foul.

Check your State and CCRs. Nobody can do it for you. 
Usually 60 days before the Annual meeting, the association mails an Intent-to-be-candidate form. If you want to be a candidate, the first step is to return it. 
30 days prior to meeting, the ballots are mailed (with a meeting proxy). 
If there are only three candidates for a three slots, there is no mailing of ballots. The 3 are automatically elected Directors. 
The annual meeting is usually followed by an Organizational Meeting where the Officers are appointed (usually directors). 
This may give you the impression that the President elects himself. He can nominate himself but the two other directors have to approve him. Same for the other officers. 
There is nothing un-ethical. If you wanted to be candidate, you should have returned your Intent on time. 
If no Intent form was mailed to owners with the first notice of Annual meeting, check your documents. If the assn. forgot to follow the procedure, contest the election. It should be done within 45 days. 
After reading your State and CCRs, email me directly if you have add'l questions.

As long as they were not candidates I see nothing wrong with the Pres and VP being on the nominating committee. As Ron said, usually you cannot find candidates to run for the open positions. Trying to members to serve on the nominating committee can be just as hard. As lkong as the bylaws and/or state law does not prohibit board members from serving on the nominating committee there is nothing wrong with it as long as they serve in the best interests of the assn. Our nominating committee is made up of board and advisory committee members each year. If a board member is uo for re-election they are not appointed to the nominating committee.

I think the bigger question is whether they notified homeowners that nominations were being accepted. If not, any homeowner who might have been interested never had the chance to run. Names of nominees might be available (I think they should be) and the committee should be able to provide a reasonable explanation of why they chose the candidates they did (experience, background, etc.) or why others were not chosen. Being open to the homeowners questions reduces the potential for unhappy members.