Sometimes I strengthen more skills when I make a few mistakes than when I make no mistakes at all. Is this just a coincidence?
I agree that it sometimes seems mysterious. In terms of strengthening multiple skills, if you get enough of the words in the other skill correct, that may be the reason regardless of whether you make mistakes in the skill you are strengthening (although maybe you are using the general strengthen).
The strength for each skill is also based on how many words you know. So, I think that the strength may go up if they give you new words to learn.