Just as the pp said that you can bring a tripod in the parks. I do bring a tripod or monopod in the park so I can videotape the fireworks, F!, WoC and the parades.
But here is the only catch that DL will have with a tripod. You can bring a tripod into the park that can fit inside a backpack or small bag. They won't allow commercial tripods (media tripods) in the park. If you bring a personal tripod that can fit inside a bag, the CMs at the security gate will have no problem with it.
Shows like F! and WoC, the CMs will ask you to level the camera of the tripod towards your head height. They do this so the camera won't bother the other people behind you during the show. I had some CMs told me this for WoC when I got a railing. I didn't like it since I am a short guy and needed the extra height to get the show.
For F!, you might want to videotape the show with a tripod on the back side of the sitting area since you will not obstruct the show from your camera. I have never seen people that used a camera tripod for F!, but I do see people with their cameras in their hand and putting it up which is annoying.