Murphy’s Law states that if something can go wrong, eventually it will. This applies very seriously to climbing Mount Fuji. For the moment, let’s forget about the possibility of the volcano erupting!
You have to be careful to avoid injury. It’s all rough volcanic rock higher up so sprains and fractures are not improbable. It’s easy to get careless as you get tired and light-headed from lack of oxygen. You should wear fairly sturdy shoes but you may have problems with blisters if you put on serious hiking boots without wearing them in properly.
You might consider taking some band-aids. The good news, of course, is that there will be lots of people around if you climb the mountain in the summer months. You’ll probably get help if you get in trouble.
Don’t forget that it is a pretty high mountain. The rule is that you lose 0.6℃ for every 100 meters you go up. That means that it will be about 19℃ colder at the top than it was at the foot of the mountain. If it’s cold at the bottom, you’ll probably have very severe problems as you go up! Even in high summer you’ll need something warm to wear at the top. Of course, that means you are going to have to carry it. You’ll also have to carry food and drink unless you don’t mind paying a lot of money in the shops on the mountain. Carrying all that stuff is going to contribute to tiredness, especially as you’re going to be suffering from lack of oxygen.
Also, as you’re going to feel cold at the top, you might be in a rush to go down. You’ll have to be careful as there are a number of routes down that go to completely different locations. If you try to climb down to Fujiyoshida, in Yamanashi, and take the path to Subashiri, in Shizuoka, by mistake, you’ll end up finding yourself about 18 kilometers from your destination! That is going to feel horrible.