Let me see if I can explain this... something that I found to be odd, and have never experienced in the past. This is a new showerhead. After installing, I noticed that about 5-10 minutes after showering, there would be a little extra water that dumps itself out of the showerhead. It's not coming out of any connections, but from where it's supposted to come out. It's not like a couple drops of water either, probably I'd guess 1 cup of water. It happens quickly, like there's a person holding a cup of water above the showerhead, and just dumps it. And this never happened with the old showerhead. Do I just have a bad showerhead? This only happens once per "post-shower".

No you do not have a bad shower head. I have an idea that you bought a larger shower head than the one that you had before. With a large shower head there is a large amount of water (about a cup full) still in the shower head when you turn the faucet off. This water is more or less trapped in the shower head by a vacuum until it can get some air in it to break the vacuum, when it is broken, just by time, then the water pours out. If you do not like this happening because you have already cleaned the shower or other reasons here is something that you can try. When you are finished showering turn off the faucet and then move the shower head into the most upward position that you can, this water should drain out as you lift the shower head.