I think this is a rather important topic/issue for both Mapillary and its contributors.
One would think that at least in those countries where public street view services exist -- Google Streetview being a good starting point -- it's ok to take pictures of public places / in public spaces. Of course it still might be regulated even then -- I have no clue of reality, just guessing what the reality might/could be. This logic would make sense (to me at least).
In short, mapillarying is ok in all publicly accessible places with below noted limits. And I think same right & limitations apply to taking videos. I have also never heard that how a recording device is mounted would have any impact to these rights.
In more detail:
You can take pictures in all public spaces which includes all places to which there is free public access. This includes public spaces of shopping malls, libraries, lobbies/public spaces of government offices and (even) public hospitals and alike. The only limitation in these kinds of "fully" public spaces is that official security guards have the right to remove individuals from such places -- and so this would end one's photographing. I don't know where would be limits for e.g. something like "grounded removal from (such) public space".
Slight limitation applies to taking pictures in individual shops, restaurants, etc in which you are allowed to photograph by default -- but businesses are allowed to choose their customers and are allowed to essentially forbid taking pictures based on that.
There is also a concept of semi-public space, which includes among others offices and industrial facilities. For those you need a permission.
Finally private spaces have a privacy limitation which also lead to a requirement for permission to take pictures. This includes publicly visibleplaces that are considered private. This might include e.g. backyards of people. IIRC there was a case not so long back where someone had been pissed off to Google enough to make a case out of their Streetview having showed their backyard. It might (or might have not) included something considered more private such as some naturalist activity -- I can't remember -- but there was a bit of a fuss, at least some media noise about it. I really can't remember if it went to court or not.
Simple web searches have good chunk of information about all this both in English and of course in Finnish. Specific pages that I checked to verify what I remembered (some of which was wrong) were this and this (both in Finnish).
With the above, I would assume that information about many individual countries is by now available online with similar searches. And I guess people mapillarying in different countries and even perhaps Mapillary at some point should do such searches to at least give an idea what the situation is in different countries. This is a good thread to share that information.