The difficulty of mastering the tenses is something that I think a lot of English speakers overlook. There's a lot of really precise and difficult-to-explain subtleties in English. (Of course, English isn't unique in this regard -- but I feel like certain things are taken for granted).

Something that catches a lot of English as second language people out is the correct time to use the gerund form (i.e., the '-ing' form). For instance,

(1) I am walking to the shops.

is clear -- it is occurring in that moment. But what about the subtle difference between (2a) and (2b)?

(2a) I live in Berlin.

(2b) I'm living in Berlin.

To me -- a native English speaker -- (2b) implies that the speaker generally lives elsewhere, while (2a) doesn't. But they're both technically correct if the speaker is, at that moment, a resident of Berlin.

There are more examples I could give. Teaching these sorts of subtleties, though, and mastering them can be very difficult.

A final example that I really like, and one that my syntax lecturer used to use a lot:

(3) She would have had to have been being watched.

Seven (or maybe six, depending on how you view 'watched') verbs in a row! Native English speakers grasp this really intuitively, but non-native speakers may have trouble parsing these into a coherent picture. To illustrate this -- try and gloss this sentence another way while conveying the meaning. If you speak another language, try and translate it! English verbs are hard.