Well. I don't really have the struggles that learners might have with the spoken part of learning the language. Obviously, being in an environment where I'm surrounded by native Korean speaking literally all day everyday, listening is actually my strongest skill, and speaking -- as far as pronunciation goes -- is not far behind. Speaking, as in sentence structure, is a completely different story. As is spelling, because I hardly see anything in writing at all, compared to how often I hear words.
The hardest part for me (besides the fact that I'm lazy) has definitely been the fact that I can hear and learn a verb, but then I have to turn around and conjugate it several different ways, depending on who I'm speaking to. It's not that the different levels of speech are so hard to learn -- it's actually quite simple. But as an insecure second language speaker, it can be difficult to get the correct one out when you're put on the spot. If there's a verb I'm more used to using with students (speaking informally), when I go to use it with an adult, sometimes it will come out automatically in the informal form. Because my brain is scanning, trying quickly to grab ahold of the vocabulary I need, and it when it hits on the word that is the right meaning, sometimes it doesn't stop to consider, is it also the correct form in level of politeness? So, when you learn a new verb in Korean, it's not one-size-fits-all -- not only do you have to mentally edit for tense, but also for level, which means, inevitably (when I'm speaking, at least), one or the other is going to come out wrong.
Luckily, most Koreans take it in stride if you suddenly bust out with an informal expression, especially if you're obviously making an effort to use polite language. My understanding, actually, is that Koreans tend to consider the levels of speech far more difficult for foreigners to grasp than they actually are. If everything else you say is in polite form, don't sweat it too much when you come out with something casual. Most people will understand that you don't mean it.
On the other hand, I've been sort of mercilessly teased about using the polite level around close friends. When I first started learning Korean, it was in a classroom environment, where everything is taught in the polite form. When it came time to hang out at the bar on Saturday night, I was the odd one out speaking too formally for the setting, with everyone ribbing me about how awkward it was. But I had no idea how to shift down at that point, and speak more casually. Now, after stopping my Korean class and picking things up more from the students than from anywhere else, as well as pop songs, dramas and movies, I'm getting much better at being able to speak casually. Maybe too much so.
That aside, as you are a classroom learner of the language, I would definitely recommend watching Korean dramas and movies to help you along. Pop songs, as well, because they are full of repetition. Of course, just passively consuming Korean language media won't do you much good. As you watch a drama, pause and listen to certain repeating expressions, phrases or words, until you can get the spelling and pronunciation down yourself. It's a great way to learn how certain words and phrases are actually used in context, which is sometimes quite different from textbook explanations. Before you start listening to a pop song on repeat, go through the lyrics in Korean and translate them into English so that you know what individual words and phrases actually mean, and they are lodged in your brain with both sound and meaning.
I feel kind of like a schmuck answering this one, to be honest, as my Korean studying has completely fallen off of late. Right now, considering things about the future, I'm not sure it's going to be a top priority for a while. But I still have benefited immensely from what I have managed to pick up here, and everyday life and interaction is much simpler and much more pleasant. So. Good luck in your studies, everyone.