A few things that I thought were badly written
Tigress finds the super secret village super fast. Did she have a map? We never know. We should have been shown how she found the village. And not a single panda wonders about how she found it, even though they were clearly extremely secretive about it.
The evil dude finds the village super fast, we do see him follow the tracks of Tigress some of the way and her smell it seems. So if she didn't go there he would not have found it so fast? And Po would have had more time to train and be with his family? When he finds the village the whole coolness of the village disappears. At the start we all thought it was something spectacular but then we find out it is actually pretty easy to find apparently.
His bird father, Mr. Ping, found out that his real father lied to him before Po told him anything about it. Po just met him coming from the bridge where he found out the pandas didn't know chi. How did Mr. Ping then know about it right away? He was not on the bridge with Po and Po's father, and we discover how he knew about it.
Po knew that they had all helped him while he was in the realm world... somehow. Again, he might have sensed it, but we are told nothing about it. He could have said: "I sensed that you all helped me while I was there!" Just a short sentence that would take a few seconds to say. And it's not like the movie could not use a few slow moments and dialogue explaining things.
There are a lot of these things in the movie but I just mentioned some of them. Seems like there is a longer version of the movie out there. At least I imagine the script was longer. It seems like they replaced some of the crucial dialogue with action or just removed it.
It all seems like going a bit too fast as Po both meets his father and discovers it is him right at the start. They could have continued the joke for a bit and let us know something he didn't know. We also see the main villain right away. He is there from the very start which takes all the mystery away. The first Kung Fu Panda has a ton of mystery, that's what makes it good. This one looks very plain. He suddenly knows chi because he needs to win. And the village learn to fight very fast. Everything happens so fast that it is more a ride than a good deep story.