But... I sort of thought that was intentional. Mugi's outrageous family and associated privileges, at least. Sort of like a running gag.
Yui being a natural at guitar... well, yeah, okay, it's a stretch even in the context of how many "convenient" things happen in anime, but there *are* many people out there with a natural gift for music. And it was made pretty clear that she's not as good as Azusa, someone with more formal training and experience.