There are a number of aspects of the Japanese language that you can use to supplement your Japanese studies, but one of the most difficult areas in my opinion is that of politeness. More often than not, anime characters care little for using the appropriate verb forms in specific situations. Probably the most you’ll ever see in terms of levels of politeness and familiarity is characters who originally called each other by their last names transitioning to a first-name-basis kind of relationship. And the most formal vocabulary is known as “keigo.”
Keigo is the kind of vocabulary you use when you want to be ultra formal, ultra polite, and probably talking to your boss. I can’t give any specific lessons as my keigo is shaky at this point in time, but to give you an idea of keigo and some of the difficulty that learning it entails, I’ll provide a few examples. The verb “suru,” to do, in keigo is “nasaru.” That “itadakimasu” you hear so often before meals is actually a keigo form of “moraimasu,” or to receive.
Again, this is not something you can develop or improve significantly while watching anime or reading manga, so in this case it is best to go through more orthodox channels.