So, things like, for instance, apposite nouns. English is odd in this, in that few of the world's more widely-used languages use this grammatical strategy: put two nouns beside each other, and one of them assumes the function of an adjective. "Peach pie", "road rage", "sand pit", and so on. And it can be maddening for new speakers of English, because there can be different meanings expressed by the ordering of these nouns. For instance, a "school night" is a very different thing from a "night school". Learning the nuances of various combinations of apposite nouns can be a real minefield.
What other aspects of English are difficult for non-native speakers? I don't necessarily need lengthy examples (being a native speaker myself), but I'd be interested in hearing from those who have learned English as a second or foreign language: what concepts did you find most difficult to master? Verb-particle constructs (e.g., "to put up with")? Orthography? Expressions of time? Plurals? Ablaut in irregular verbs (sing, sang, sung)?
As examples of such difficulties, consider Russian verbs of motion, or the Finnish noun declensions, or the honorifics of Korean and Japanese. I'm looking for the factors that mark the differences between the casual learner and the expert.