One thing I've noticed is talking about phrasal verbs. ESL students really struggle with phrasal verbs. They are notoriously difficult to parse and understand. Take this one for example:
What do you mean, "off on?"
I can't figure it out. (separable)
NOT I can't figure out it.
We'll check out of the hotel tomorrow.
We'll check out of it tomorrow. (inseparable)
NOT: We'll check it out of tomorrow.
Regarding usage, American and ESL students tend to have opposite problems: ESL students will often overuse Latinate verbs in conversation when a phrasal verb would be more natural ("I'm trying to determine which apartment to rent" vs. "I'm trying to figure out which apartment to rent"), and Americans often overuse phrasal verbs in academic writing when a Latinate verb would be much better ("The recession ended up costing tax payers" vs. "The recession caused higher costs to taxpayers"). This is helpful to make both types of students more aware.
I think this is a lesson that belongs in mainstream writing classes. My reasoning is this: Many American students have been told, "don't write like you talk," but what exactly does this mean? The actual grammatical features common to speech need to be pointed out to them. I've taught this particular topic to my American students and once they're paying attention to this, I've noticed them self-correct their own writing, and it begins to take on a more academic tone. This is especially helpful for students with a limited vocabulary--it's more challenging for them to substitute their phrasal verbs with their Latinate counterparts, but at the very least, they have a more measurable way of not "writing like they talk" (whatever that means).
Have a good one, and good luck out there!