In what ways can I improve my writing mechanics?

[arewethereyet]

Grammar is not all that important in the real world, unless you are planning on entering a field of work associated with English and literature. I am also certain a history professor is going to be less concerned with grammar than historical facts, because chances are s/he does not understand grammar as well as an English teacher. I would not worry about it too much so long as you are doing well enough in the area. Perfection, after all, is unnecessary.

Being able to write properly is important depending on what your profession will be.  Many job listings specify the need to be able to communicate well both verbally and in written communication.  How you speak when having a beer with your buddies is a whole different thing.

Being in graduate school indicates a high level of education and people are going to expect a person at that level to be capable of writing properly.