We've played a few games and there were a couple of accounts. In one, a player (correctly) surmised that no one was a Cylon in the early game, so he took a series of actions to bring the humans to low food, got himself executed, and came back as Boomer so as to double his chances of becoming the Cylon.
In another case, I was executed on suspicion of being the Cylon, which allowed me to demonstrate that I was in fact human. I was able to come back as Gaius Baltar (original) and use my Cylon detector. This gave me a great deal of power because not only did people know I was human, (Baltar's typical problem) but I was also able to identify someone else with 100% accuracy to the group.
We are proposing the house rule that, upon execution, you draw the replacement character at random instead of choosing. We are also toying with the idea of allowing the random draw to include the Cylon leaders in a game where there is not already a leader and giving said leader a sympathetic agenda card.
The reason for this proposal is that the ease of getting yourself executed, proving your loyalty, and coming back as a character of your choosing seems too powerful.