I learned mostly by doing, through undergraduate research, and then in graduate school. This was far more effective than lectures or books, though those are very helpful for getting started. I had one class that covered an overview of lots of the technology, and was lucky enough to have access to preprints of Koller & Friedman's book as a reference to fill in any gaps. I also read Judea Pearl's book on Bayesian Networks fairly early on.
As far as everyday reasoning, it made me somewhat more skeptical of long chains of A --> B, !B therefore !A, type of thing. It's easy enough to model this type of logic as a special case of PGMs. And the causal stuff is extremely useful for making me skeptical of arguments of the sort "If we did X, then Y would happen," and also how and when correlation is causality. Don't have any pat examples though, it's just something that infuses my thinking, such as learning about biological evolution.
It's definitely the hardest one I've taken there. Most of the difficulty comes from the density of the lectures. She moves fast and takes it for granted that you're piecing everything together as you go. You're probably not, but at least you can go back and watch it again if necessary!
Hinton's Neural Network class was very challenging for me too, mostly because many of the concepts were unfamiliar to me. But again, I could re-watch whatever I needed to in order to get it.
