Answer by Martin Schneider:
To a degree: yes.
Generally speaking, as a foreigner in Japan, you are under a usually imperceptible – but nonetheless constant – form of mild observation.
Note that with less than 5% foreigners present in Japan, you are a bit of an oddity to begin with. And if you are sitting in some metro car, it's not wrong to assume that a good number of people will be constantly throwing glances your way. Usually while you aren't looking. For some foreigners, this can (and has) even lead to forms of borderline paranoia.
Now, mind – mostly, this is not because people would expect you to suddenly stand up, whip out a gun and start screaming&shooting or something. Mostly.
No, instead, the reason here is that Japan is a sociotope with tons of invisible rules. Some of them are "only" unspoken, while others are so implicit that even a Japanese would rarely be consciously aware of them – and yet he instinctively acts on them. As a foreigner who did not grow up there, you will be breaking these constantly.
Not because you intend to be rude – no, you just can't help it. You don't know most of them, and even the few you might know can be hard to use properly sometimes.
Maybe because you pass people on the "wrong side" on the sidewalk.
Maybe because you aren't aware that the controller in the tram line comes every 30min and don't take out your tickets in advance.
Maybe because you haven't internalized the iron rule to set your cellphone to mannaa moodo as soon as you board a train.
Maybe you don't even know what mannaa moodo is.
And so on…
Accordingly, the Japanese around you will – usually rightfully – expect you to be a source of constant tiny but inevitable troubles. This is anathema to the general Japanese notion that people are supposed to be aware of and even anticipate the needs of everybody around them, to allow smooth interaction.
In other words, you are a constant micro-disturbance in the harmony-optimized Japanese social ether.
And that's the biggest part of why people throw you glances. On one hand they are indeed a bit uneasy around you, on the other they always ready themselves to fill the gaps, to pick up your slack… often so well that you won't even notice most of your tiny transgressions. Now, it's up to you whether you consider that "bad reputation", but the result is pretty much the same.
That being said, there are also a few more extreme aspects to this "foreigner attention":
All trappings of the modern world aside, some (especially older) Japanese still hold very traditional, often fairly Japan-centric world views. To the point that some of these views may seem provincial or even silly to the modern eye.
But they exist, and you will be judged by them. And like it or not, no matter where you go in Japan, you will always be a blatant stranger.
And of course strangers are, by provincial default, suspicious.
Who knows why they are here?!
Who knows what they might do?!
Even more so if it's a 30ish male who apparently travels alone (like me). Of course no one will ever walk up to you and straight-out ask you what the heck you are doing in his street/park/whatever. But hey, it never hurts to be careful, you know…?
In the worst case, this can sometimes lead to some quite awkward moments.
Which is especially painful for foreigners who generally feel an affection towards Japan.
Anecdotal but illustrative case:
In 2009 on the second day of my first Japan vacation, I was visiting. Back then it was still a top-3 sightseeing spot in Tokyo (today the is more popular, but I digress).
As you can see, there is a little bit of greenery around the base of the tower, maybe not quite enough to be called a real park, but enough to have a handful of tree-covered pathways, a playground and a few benches.
Fate wanted it that I mixed up two streets and first missed the normal road that leads up the tiny hill the tower stands on. And so I found myself in the park-like part on the far side. There were some pigeons, a kindergarten class playing on the playground, and a few people sitting here and there on the benches.
I was standing around looking for some passageway that might take me to the tower base, when a movement caught my eye. I saw how the young female kindergarten teacher had quickly positioned herself between me and the playground – and was now straining to usher the kids to play on the attractions on the other side of the ground. And that playground was at least 50m away.
What I can't forget is the expression on the young womans face.
It was concern. And fear.
Granted, I stand 1m 95cm (6''4) tall.
But never in my whole life have I felt so much like a boogeyman.
That one hurt. Especially for someone who was still new to Japan and brimming with positive feelings towards that country.