I kind of implicitly assumed we are not talking about missing the obvious stuff (like someone staring at you angrily in a 1 to 1 conversation). That would probably best be explicitly learned by flashcards.

Everything but basic emotions has a lot of hidden states and the tracking becomes much more of a thing. But that state is not all that hidden. You actually know a lot about the people in your life. 
The hard part is coming up with enough hypotheses and not separating true from false. I call it to myself 'generating social conspiracy theories' to get rid of my inhibition to state a bad theory. Whatever you come up with usually will not be too bad. Evaluating the truth of 'my colleague is stressed' is usually easy. But it will make you aware that they are or aren't and how that influences their behavior. That is what you actually learn and what will make you aware of their stress in the future.

I never felt like there is a lack of 'obvious' things to become aware of. Either things are so interconnected that everything is kind of accessible with enough layers of such perceptions, or I am playing on too basic of a level of this game to get to interesting cases. I feel like I am learning some deep art, so I am probably a total beginner to something most are much more capable at just by using their intuition.. 
The disappointing part of course is that reading strangers minds is hard with huge error bars and reading huge parts of the mind of close people is basically expected.

I might be arguing something totally besides Lsusrs original point, but I do not think that facial expressions carry very far and this (cognitive empathy) does the thing he seems to be after. 

The test scores me as 'normal' with 29/36. I remember doing a similar (maybe the same) test and scoring decidedly below average about two years ago.

I understand the attraction of having this skill trainable in its own context like flashcards but consider it a false shortcut.  I think it is more about directing attention. 

Setting aside a few cycles of my attention to practice in every day life worked for me and I think it should be wildly superior to treating it as a problem of categorizing features.

1. You get so much more context to infer from and that hints at things you should be able to detect. After all, the true version of the skill is not 'detect <basic emotion x >' but 'emulate people roughly and extract information'. For that to actually happen you want to keep detecting new features and explore them. Not be x% better at separating desire vs. attention.
2. You also train actually using the skill in the background (that is becoming aware that a person feels x instead of just being able to answer if you should happen to ask yourself about what they might feel). This is also the hard part in my opinion. 

It is frustrating, but every time I want to modify anything about my mind it comes down to a mindfulness exercise.
 
EDIT: 1. basically says this is a case of What Are You Tracking In Your Head?

I tried similar things more than once. 
It is just as frustrating as learning to not let attention wander when meditating, but on a bigger time scale.
Edit: Also just as worthwhile I hope

The vagueness of your observations makes your question completly meaningless.