Also, during this same Assessment Center Exercise, prior to the beginning of a session, I was sitting next to a Captain from another agency when the lead consultant leaped (literally!) into the room and upon seeing this Captain came rushing over to him and, in front of other candidates (me included), proceeded to expound on his impressive resume and how happy he was that this Captain was testing for the position. At first, I thought it was part of the stress program associated with the Assessment Center, but as this consultant went on and on about this candidate's achievements, I realized it was just bad judgement on the part of the consultant. These actions made me realize that I must be more conscious of the performance of others during the Assessment Center (especially, when I was involved in group discussions or other interactive dimensions with this candidate).
These are just a couple of examples with which I was personally involved. Of note is that on the positive side, they did assist me in being better prepared for future Assessment Centers.
Later, the raters may ask you to explain some of your actions during these various exercises. Don't become excessively nervous. If you have a reason for your actions, which I assume you do, give it because these exercises are designed to display who you are and allow the raters to view the way you accomplish your assigned tasks. Oftentimes your explanation could be outstanding and the raters may question it only because it was not the way they would have completed the task, and they know that there is always more than one way to complete a task.
Assessment Centers, if done properly are expensive and in today's economy may be excessive not to mention time consuming. I don't personally like to use Assessment Centers, nor did I during my tenure as Chief. But remember it does not make any difference what I like or don't like - it depends on what your administration or personnel department wants.
So the best advice I can give you if you are faced with participating in an Assessment Center is to not be upset but to welcome the chance to prove that you are the best candidate no matter what testing process your agency utilizes. Prepare properly and stay positive!