I hate lay/lie issues -- I literally have to write down all the conjugations for both words to ensure that I am using the correct one. I am sure that verbally, I am wrong most of the time. In written work I am highly conscience of subject verb agreement with indefinite pronouns, but I still find myself typing quickly and writing something like: Everyone should work hard on their essays. I know full well "their" should be "his" or "her," but I slip up sometimes.
In a movie the other day I heard "After he had woken," and I thought that sounds so wrong. But, it is merely archaic. Nevertheless, I sometimes stumble around trying to decide whether I want to use a form of wake because woke and waked sound odd, too. So, I just say __has awakened. Actually, I pray that people are not sleeping when I am around. Or, at least, that they wake up on their own, so I do not have to use that fearful verb.
Some rarely used subject/verb agreements--one that are in English texts, but not often used--are at times tricky. But, having conjugated pages and pages and pages ad nauseum of verbs in high school under the tutelege of ancient Latin teachers has served me well through the years. Those same grammarians required us to serve equal time creating tomes of diagrammed sentences! But, this activity has preserved me from the influence of the dialectal horrors of the part of the country in which I now live.
Grammar comes pretty easily to me, but I have a few words that I struggle to spell correctly. "Privilege" is one of them; I always want to switch the Is and Es around, and I used to always stick a D in there somewhere. I learn best when I'm getting some kind of relationship into my head. I can remember lie/lay, for example, because there are two of them, so I remember them in relation to each other. I remember how most grammar rules work because I can put them to use in several situations. But when there's just one fact, and I get it into my head wrong when I first learn it, I have a terrible time getting it back out.
I can never seem to remember the rules for such things as lay/lie, hang/hung, good/well, affect/effect and etc. Just when I think I have it clear in my mind the insidious voice of doubt creeps in, and I begin to wonder all over again. I also sometimes slip into the passive voice while trying to create more variety in my sentences.
I would say that some of my biggest problems are also the dangling modifier. I also struggle with subject and verb agreement at times in written work. I think my struggles are usually more related to mechanics of writing as opposed to grammar.
I remember when I was training to teach English as a Foreign Language and I encountered plenty of items of grammar that instinctively I knew how to use but when it came to explaining them I entered into an absolute nightmare world of no return. For example, phrasal verbs and the subtle but oh so important difference between phrases like "they are putting us up" and "they are putting up with us". Also, the 3rd conditional. We speak a complicated language and I for one am glad I did not have to learn it in school!
My greatest grammar challenge is probably not going to be the same as yours, so I would encourage you to answer this for your professor from your own experience. Over the years I've struggled with the classic kinds of errors: lay/lie, comma splices, -ie or -ei, subjunctive mood. By far, though, the grammar issue I am most consistently challenged by is the dreaded dangling modifier. I'm not sure why, but this is an error I make with alarming regularity. I've learned to catch them, but I really have to work at it and I'm certain some manage to sneak through in my writing.