I personally prefer to call them not negatives but "differences," or in more severe circumstances, "challenges." I feel like it just helps your state of mind when you get culture shock and feel very emotional about these things. I'll address the big ones at the end but first here are some small differences that I found to be more somewhat irritating from time to time.
-Clothing is often one-size-fits-all, and even if it's not sometimes the larger sizes are still not that large. This requires very strategic shopping if you don't fit into the standard Japanese shape, or possibly just importing some of your clothes (as I had to do for very specific items, otherwise I just purchased things that were designed to be baggy on smaller Japanese people that fit me just fine). Changing rooms are also just like a shower curtain around a pedestal so I tried to avoid ever trying things on.
-Do you like camembert? Because that's the Japanese equivalent of American cheese and it's all you will ever get on anything you order. Whenever I wanted a different cheese, not even a better or finer cheese, just like a cheddar, I had to seek out a specialty cheese shop.
-Despite "variety" being the name of Japan's most beloved TV genre, there isn't a whole lot of variety in Japanese TV in general. Since I was there, they have gotten video streaming services like Netflix and Hulu so you can remedy the boredom that may come from a never-ending feed of talking heads on TV, but it's still something to be aware of.
-Stingy indoor climate control. I'm from the US and I'm used to central heating and air that constantly maintains indoor temperature, but that doesn't exist in Japan (neither does good insulation, it seems). They have room-unit air conditioners and they have space heaters, but they're very reluctant to use either of them because of the price of utilities, especially in winter. Stocking up on reusable ice packs and warm roomwear are a must to offset the temperatures.
-Food you may be used to eating in your home country is often different in Japan and, in some cases, unpalatable. I had people send me things regularly that I missed since I could not find a comparable Japanese equivalent.
-If you have any dietary restrictions or even strong preferences, you may have trouble being accommodated in that regard and run the risk of being perceived as rude because you refuse to partake in something (just always say you have an allergy, even if you only don't like it, because at least then they won't take it as personally).
-In my experience, I found it difficult to make really good foreigner friends. It's not impossible to make Japanese friends, but it's easier to make a connection with people who already share similar cultural experiences and languages as you. Still, that makes the pool of people really small, and I didn't find too many people that really enjoyed being around most of the time.
That's all I have off the top of my head. I'm sure there are others, but basically homesickness was more of an issue for me than cultural differences, as I suppose I have the personality type to adjust to living there as a foreigner, but to touch on what others have said:
I really liked being the perpetual outsider most of the time. I found it quite liberating, actually. People didn't bother me when I didn't want to be bothered, and I was often given a little more grace in social faux pas than I would have been given otherwise. I also kind of liked feeling like I didn't have to be as invested in politics or social issues because they usually explicitly excluded from dialogue. Those things can get tiring after a while, after all. Now, many people aren't suited to this sort of lifestyle, and you do need a really good friend or two there to share in your outings and life to make the solitude more bearable, but I personally didn't find it as painful as many do.
Oh, and yeah, if you're outside of the Tokyo metro area, you're going to get stares. Again, it didn't really bother me. If anyone stared a little too long I just made a weird face back at them, which resulted in either laughter or embarrassment from the offending party, but in either case they recognized their mistake in looking at me a little too much.
Bureaucracy, education, employment... eh. Everyone has to go through it and it's confusing and everyone has strong feelings on it, but whatever. Just do what you're supposed to do, same as anywhere.
The main thing to keep in mind is that none of the cultural or social behaviors that foreigners often perceive as negative in Japan exist in a vacuum. They have motivations and reasons for doing the things they do, even if they don't make sense to us. You can make the most of your situation by trying to understand those motivations and, if possible, trying to demonstrate that they might be wrong for believing one thing or another. The staring thing is a good example, showing them that they're being rude even though they're only doing because they almost never see someone who looks like you and they're thinking about who you might be; or when people in stores avoid you because they don't think you understand Japanese and they don't have enough confidence in their English to try to sell something to you, and then you ask them for help and they're 100% on board. It's so important to keep a frame of reference that you are always a guest to them, no matter how long you've been there, and you are receiving their goodwill by being allowed to stay there, which is incredibly humbling. So humbling, in fact, that most people can't handle it. I'd suggest going over on a tourist visa and seeing how well you fit in, how much you like being the outsider, before committing to anything with more permanence, but for what it's worth, I didn't find it particularly difficult to live there when I came in understanding where my "place" was.