You are right about warping. I inspected a five layer board I have already designed and fabbed. There is a little bit of warp. Not enough to affect performance this time. From now on I will only design with an even number of layers.
I have also become aware that the amount of copper on each layer will affect warping. So now I must take care to put copper where it is not needed electrically just to fill spaces with it. An while doing this I must be consider increased capacitances where it is not wanted and cross talk problems it may also cause where a copper fill area is not grounded or connected to anything.