As others have said, it's not really 'smoke'. The flue gas from a well maintained gas boiler shouldn't contain much of concern. It's visible because of the water vapour content, and you see it more with a condensing boiler because it cools the flue gas to the point where it at least approaches the point where it condenses from dry steam (invisible) into 'wet' vapour/mist (visible). It's also more visible in cold conditions, like we've had this week.
The main substance in the gas from the flue will be nitrogen. This makes up 79% of the air around us and still 79% of the flue gas, as it plays no role in combustion so passes through the boiler unaffected.
The next biggest component will be carbon dioxide at about 8-11%. This is present in the air anyway, but in much lower concentrations. It isn't particularly scary stuff - you produce it in your body and breathe it out. Don't confuse carbon dioxide with carbon monoxide, which is very different and is what your detector will be looking for. A well adjusted gas boiler shouldn't produce any significant amount of carbon monoxide. Even if the neighbours' boiler did produce some, it would quickly disperse outdoors.
The other gas coming out of the flue in significant quantities will be oxygen. This is obviously a good thing. We need it to live, and extract it from the air using out lungs. Air is normally about 21% oxygen. The boiler uses most of it to burn the gas, but there will still be about 2-6% oxygen in the gas coming out of the flue.
I can't personally see anything to worry about in the photo you posted. The plume from the boiler looks to be coming from a point that's not all that close to your window. At a guess I'd say it's at least a metre or so away, judging by where the boundary of the side return extensions sits.
By all means get someone to take a look and reassure you when you next have your own boiler serviced, but I'm sure you're just being understandably but unnecessarily cautious here.