When Mulan reads the Final Admonition and reads some of it off her arm, it was written in simplified Chinese. However, simplified Chinese was created in the 1950s. Mulan should have used the traditional Chinese symbols.
During the finale, Yao uses a banana as a part of his disguise. However, the banana is the sort of yellow and thin specimen a modern Western audience would recognize. This kind of banana cultivar would not be bred until centuries later. The bananas available in China in the era the movie is set in would have been rounder and of a different color.
The primitive bamboo cannons (huochong) are known from AD 1132 onward, when General Han Shizhong used them in a city siege. The legend of Mulan is set around AD 600, and Huns are active a few more centuries before that. This weapon is way too advanced for era shown.
When Mushu is chasing after Cri-Kee after Cri-Kee insults him, he says, "Whatcha mean, a loser? How 'bout if I pop one of your antennas off and throw it across the yard, then who's the loser? Me or you?" However, his gestures are exactly the opposite, first pointing to Cri-Kee, then to himself.
When Mulan, Ling, Chien-Po, and Yao dress up as concubines in order to defeat the guards to get to the emperor, Mulan is seen to have a green fan. But when she is on the roof with Shan-Yu, she pulls out a yellow fan.
When the remaining Huns emerge from the avalanche (observed by Mulan) and look down from the pass onto the Imperial City, the City is oriented with its front gate facing the pass. Moments later, when Mulan rides off to warn the troops, the Imperial City appears to have rotated, so that the palace is on the left and the front gate on the right.
Before the matchmaker appears from her shack, the girl with the green parasol is squatted on the left and the girl with the pink parasol is on the right. After the matchmaker reappears at the front door, the two girls have switched places.
During the fight on the balcony at the Palace in the Imperial City, Shan-Yu knocks Shang unconscious and throws him. Shang lands on his side, when we next see him, he is on his back, and then on his front when Mulan runs to him.
When Mulan and the other four girls are lined up in front of the matchmaker's house, they are at first lined in a V-formation, but when the matchmaker appears, they are in a perfectly straight line, then to a somewhat V-formation when the matchmaker and Mulan reappear at the front door.
When Mulan is pulled back onto the cliff by Chien-Po and the other soldiers by the rope, the rope is tied around Khan, her horse. But when Khan walks away, the rope is still tied to Khan's body, but he moves away freely even though the other end of the rope is under the soldiers.
In the Imperial City, Yao and Ling go down the rope from the balcony at the Palace into the crowd below before Chien-Po and the Emperor, yet they have just landed when they call back to Mulan, who is still on the balcony.
When Shan-Yu knocks Shang out on the balcony, Mulan is standing with a cloth over the rope after sending Yao, Ling, Chien-Po, and the Emperor down into the crowd. We see Shang landing on his side after Shan-Yu has thrown him, then it cuts back to Mulan as Shan-Yu approaches her, but the cloth she had in her hand and over the rope has disappeared.
Neither Mulan nor Shang are shown to have a bow before or during the avalanche, yet when Mulan catches the arrow with rope that Yao fired, she pulls a bow out of nowhere and uses it to fire the arrow back up to the other soldiers.
The Huns could not have been the enemy of Mulan and her allies. The Huns were pretty much done by 469 CE and spent their time attacking the western and eastern empires of Rome, not the Chinese. The invasion of China that Mulan is alleged to have helped fight occurred in 600 CE. The Gokturks were the likely opponent that Mulan would have faced.
When Shang and his men are trying to break down the doors, they take the right statue which has its paw on a globe, meaning it is the male lion and is ruling the world. The statue to the left should have its paw on the belly of a lion cub, symbolizing a female lion with the children she will raise. However, the left hand statue also has its paw on a globe.
In the movie, the floor in front of the front door to the palace is the same height as the floor in the palace and there is no door sill. In real palaces in China, there is a small, six inch wide, foot tall sill on the floor between the outside courtyards and the rooms of the buildings to prevent invading enemies from running through the door. This worked because the leg pads and armor of the soldiers at the time were so heavy, it would take a lot of effort to lift their legs that high at a run.
When Mulan is on the roof of the palace she is standing on the main roof beam which appears to be about 18 inches square. Seconds later Shan Yu rams his fist up through the roof and the roof beam. It would take several tons of force to do this, far more than even a strong man could generate.
Chien-Po is a normal human who demonstrates anti-law-of-physics super-strength by lifting seven soldiers from the cliff and also by holding Ling and Yao with one hand while searching for Mulan in the snow. This absurd personage is a classic stock character in ancient-war genre movies.
Shang leaves his sword in the mountains with his father's helmet on top of it, but when the Huns jump out of the paper dragon at the Imperial City, he pulls a sword out of its scabbard. However, it's possible he was borrowing the sword of another soldier or had acquired a new one while in the Imperial City.
When Mulan initially performs poorly at the training, Li Shang dismisses her and tells her to go home. However, she is reasonably young and fit, whereas her father can barely walk, so he certainly wouldn't have made it through the training and so there was no need for Mulan to be concerned enough to take his place.