in the process of updating my html to html5, i noticed that the inheritance behaved a bit strange. i’m not sure why links in the ul li lists have matched css rules with blocks that have nothing to do with it.

eg in screenshot 1 (aside), it takes over styles from the footer (but out of the screenshot also from role=navigation)

in screenshot 2 (footer), it takes of styles from the aside (and also from the screenshot also from role=navigation)
why does it do so?
In you first screenshot the css that gets applied is used on #footer #footerGrid ul li a, a:link,a:visited. By seperating this with comas you are having 3 different css selectors:
So this gets applied to the footer section, but also triggers on a:link and a:visited. And the same goes to your 2nd screenshot vice versa !
documentation for that: