About the term lengths. In team Merlot we had 15 turns between each of the votes for the King. It seemed to boil down to approximately one vote per month, which wasn't so bad. However, I don't see the point of having to vote for these positions that often unless there is a need for it (i.e. someone calls for a vote, or someone resigns from a position).
In my opinion we need to consider a few things. Do we want to have a set amount of turns between each vote? The most obvious advantage to this is that if you are not happy with the holder of one of the positions, you don't have to go out and tell everyone, which means there is less of a chance of any bad blood between team members. The drawback is that someone needs to set up votes every X turns, which may lead to a whole lot of work just to let the incumbent get a vote of confidence (which again may be an advantage too, as the incumbent feels he still has the support of the team).
The other way to do it is to have some sort of agreement on how to deal with it if there is someone who is not happy with the holder of a position. This has a very obvious drawback, as already mentioned, where the person who is unhappy needs to tell the team about it. Few people like to be told that "Hey, I'm not happy with the job you're doing", so this is risky as it may antagonize people in the team. One way to deal with this is to appoint someone who can deal with this in PMs. It would need to be a non-minister, or a separate minister who would be responsible for only handling matters like this, and nobody except that person would know who asked for a vote to be called. In that case a general vote could be called, so that it was not immediately apparent what position the vote was called for either. It would still, however, not entirely remove the possibility for antagonism. Indiansmoke was replaced by slaze as the King of Merlot in the last MTDG, and did not post a single post in the Merlot team forums after that. He may of course have talked to someone on PM, but as far as the general team went, nobody knows how he felt about it. This also creates a lot of inefficiency, so I'm dubious as to how well it would work in the long run.
What we need to realize is that no matter how we do it, there will always be the possibility that someone who is replaced from their post may feel bad, and lose interest in the game. We also need to take into account that we cannot really take that into consideration if a person who is elected does a bad job. Hopefully those who have nominated themselves to these positions are aware of this, and are adults enough to not leave the game over it if they are replaced. The way I see it our team is based on a democractic principle, and these positions are a way to make the team operate more efficiently. As long as everyone keeps this in mind, and do not put too much prestige into holding one of these positions, I think we'll be fine no matter how we choose to deal with it.