I rewatched Mulan the other day, and boy, is that movie sketchy about where everything is located, during the ending.
1. The army leaves for the Emperor's Palace. Several hours later, the Huns (and Mulan) leave for the palace. Somehow, the Huns beat the army there, while Mulan arrives at the exact same time the army does. Considering that Mulan is the only person on horseback, and the others are on foot, this makes no sense unless the army purposely took an extra-long route.
2. Our heroes struggle to break into the palace. When they finally get inside, it turns out that Mushu is already there, perfectly positioned to hurt the villain's hawk and make a pun about it. Um...how did Mushu get inside before Mulan and the others did?
Furthermore, Mushu flies to the fireworks tower on a kite. The next time we see him, he is on the other side of the palace roof, opposite of the fireworks tower. Either there are multiple fireworks towers, or he does a lot of moving around off-camera.
3. The Emperor gives Mulan a medal and the villain's sword. The sword was last seen, holding the villain down on the roof, so he could not escape his big death scene. Since the Emperor has the sword, he must have climbed up to the roof to retrieve it, just so he could give it to Mulan.
Also, he says, "I've heard a great deal about you, Fa Mulan". Um...when did that happen? We literally see when the army arrives in town! There was no time for them to casually chat with the Emperor about Mulan's backstory.