In particular, early in the film Mulan is dressed as a bride. Her face is painted white and the outfit she wears looks like a Japanese Geisha. Later in the movie the Cherry Blossom becomes an important metaphor.
Well, it is important to understand the cultural transmission that happened between China and Japan since envoys were sent from Japan to Tang China in 607 AD, and also the cultural transmission even before that. Japan absolutely became engrossed in Chinese cultural artifacts and beliefs. A great example of this is the fact that Japan, despite having differently developed phonetics, adopted Chinese characters it still uses today. Many of the words still sound the exact same, like the word library in Chinese, Korean, and Japanese. Another great example is Japan's intense tea ceremony culture was imported from China by Sen no Rikyu in the 1500s and had imported various forms of tea far before that. Architecture, art, philosophy, and even religion were largely adopted or adapted from China.
Chinese clothing, and fashion in general, were extremely popular in Heian Japan (794-1185) until potentially the Edo period, but the Kimono was thought to be adapted from the Hanfu Chinese dress of the Tang dynasty. They look very similar but do have differences. For example, modern Kimonos almost always have straight lines and Hanfu will usually have curved lines when you lay them both out. Chinese women also powdered their faces at various times throughout Chinese history. Really on this point, the show is not so inaccurate, because China and Japan had clothing that can be confused for each other because Japan borrowed and adapted dress/fashion from China.
In the show, the flower is a Magnolia flower, I think maybe a pink lily magnolia flower. They are a favorite of symbolism in China, just as they are in Japan. Also, Mulan's name in Chinese means Magnolia tree 花木蘭. So, the symbolism is actually pretty deep with the father bestowing a bloomed flower.
The movie is based on The Ballad of Hua Mulan, with the overarching plots being the same, and was heavily criticized in China for inaccuracies to the myth and history its based in. It seemed Americanized to many Chinese, but I have not heard criticisms about it seeming Japanized. I hope this answers your question. I have studied Japanese culture in Japan for the past two years now, and I do not recall there being any instances of exclusively Japanese artifacts/culture in the film.