Maybe you counted the ngons as one (Frank certainly did because I'd bet on it that he saw all of them). They are visible at 2 other connections if you start from the one Frank pointed out. The connection above seems correct, the others may or may have not that same ngon. If you look at the second picture you posted, you can see from the moved edges, that you probably had the same problem with some points on the downside. But it doesn't matter in this case, and to be honest, I wasn't even sure if they were not intentional (sometimes a model looks perfectly correct with such a ngon, but doesn't, when it is corrected).
About modeling with booleans in general:
For poly-modeling (non-subd) I use it all the time. For me, that's where it shines.
For subd-modeling I use them from time to time, a bit more drill or stencil (you just "imprint" the conncection from one mesh to the other. It's easier to clean up and can then be bridged or beveled in), always when I do not have a "better" method at hand. For me it's all about being faster, which isn't just a question of technique, but also of exercise, personal preferences, the way you're wired, your knowledge, the tools your software offers. Mostly it's just habit. In "production mode" I try not to think about what I do, I just do till I run into a problem and actually have to think about the best way of solving it.
I also have a "learning mode" for which I look at lots of tutorials, from beginner to professional, just to see how others tackle a problem. And in "experimenting mode" I try to find the methods that are best suited to me, like doing a model (or a difficult part of it) several times over with different methods, often just to see with how many of them I can come up with. In exercise mode I try to incorporate some new learned or found methods with doing the same thing several times over the same way. And you doing your boolean bit certainly made me try out such things a bit more, but very often I just know other ways I'll always be faster.
But do not get me wrong, I find it always interesting how YOU do things. And I'm not above it to steal any method that's fitting me
