I have found out what went wrong. Came across this explanation while reading about an unrelated model (paraphrasing). The problem was with post-rescale printing. The width of the scanned A4 sheet is 210mm. A regular home printer can only print 200mm in width. However the page is not scaled proportionally, but squeezed width-wise only, thus distorting the shapes.
I have noticed that parts from the same page didn't fit properly, thus the error was not with scaling itself. After reading about the printer distortion, I went back to check and sure enough the parts were positioned perpendicular on the sheet.
This was after the frustrating and quite discouraging wing assembly. After that I gave up on keeping it clean and finished the rest in a couple of evenings.
The model is not presentable enough to keep as is, and patching it would be a huge hassle, I will probably damage it some more, weather and rust paint it, and have a little wreck photoshoot, something along these lines:
To be honest it is a bit of a relief, because it ended up larger than I expected - wing span of 25", and defending it from cats and a toddler would be problematic... After the photos I'll give it to them for demolition :p