I'm probably missing something glaringly obvious, but this thought occurred to me: yes, it's inconvenient not to be able to selectively edit your photos on the photostream to remove unwanted content. However, as I understand it, this photostream doohickey only works over wifi. So, if away from your normal location and you are taking photos just make sure wifi is off or you're out of wifi range (very easy here in the UK - not tripping over public wifi signals every 2 minutes). You can then edit / remove any unwated images before you next enable wifi.
This is not a perfect solution by any means. It wouldn't fix the issues like surprise weekends away screenshots showing up since chances are you're on your own home network when you do this. Nor would it stop that photo of a semi-naked <<insert celebrity here>> being synced to all your iOS and Mac OS devices if done when connected. And you really don't want to be taking photos of your illicit liason! In this litigious age I wonder how long it'll be before someone tries suing Apple after a divorce is caused / a child is shocked by inappropriate content on the photstream.
To be honest, when I first read about photostream I don't remember reading that it would also upload any images you download from the internet / save from an email or screenshots of your iOS device. Personally I don't class those as 'photographs' and I'm sure it was marketed as "photostream stores your last 1000 or 30 days of photographs". It didn't say "images". To me a photograph is something I deliberately take with the camera. But maybe I'm being picky.
Mainly because I get a decent data plan I tend to have my wifi off on my phone most of the time, only enabling it to use the Apple TV Remote so it's not a big issue here.
But, there's the temporary solution anyway - keep wifi off unless you need it. OK, we now have Find My Friends insisting wifi be on to improve accuracy which muddies the waters a bit more, but wifi off will still help ease the photostream issues.
After scanning the posts again before submitting this, I suppose this is similar to the "airplane mode" suggested but with the added benefit of still being able to receive calls if required.