Deliberate mistake: During the movie, when Mulan is just a girl, you can see that her eyelashes extend beyond her eyes. When she is pretending to be a boy, her eyelashes are short (this makes perfect sense). But when she is in the medical tent her eyelashes are long even though she had no time to put on makeup. This is deliberate though, because without it she would have still looked like a boy, and just pulling her hair down wouldn't make her look any different (since that's how she looked in the pond). So they had to change her eyelashes to make her look more girlish.
Deliberate mistake: When the troops are marching towards the village which is now destroyed, they would have noticed it long before they actually do. (The makers did this on purpose so that the song "A Girl We're Fighting For" would end on a good note).
Answer: For the reasons stated. He believes him to be a highly competent soldier and trainer. While this opinion is probably influenced by Li Shang being his son, it does prove to be correct, as Li Shang's training is what allows the small group to succeed in battling the Huns.