The new children's zoo area at the zoo is very much worth seeing. The invertebrate house is fantastic, although apparently its star attraction, the coconut crab, is dead. (GET ANOTHER ONE, SAN DIEGO!). The adjacent new hummingbird aviary is full of great South American birds. The new Komodo dragon complex is good.
If you have time, you might want to take the San Diego Zoo bus tour which is now free with admission. It will show you parts of the zoo and views of exhibits that you won't see otherwise like Fern Canyon, although nothing "must see" if you don't have time.
I haven't watched the San Diego Zoo animal presentations in the Wegeforth Bowl for years, but I always found them to be high-quality and worthwhile.
The big news of course is that giant pandas are back at the zoo, and you will have the challenge of fighting the crowds to see them.
The Birch Aquarium has little penguins now. From pictures it looks like a nice exhibit.
The Safari Park is in the middle of building the new elephant area, so be prepared for heavy construction obstructing parts of the park.