Use of "their" referencing a singular noun -- e.g. "A teacher should put their stuff away here" rather than "A teacher should put his/her stuff here" (ironically, I just saw that on this thread).
Not using "were" for a conditional (I don't know if I am using the correct term) -- e.g. "If I was rich, I'd buy a big house," vs. "If I were rich, I'd buy a big house."
Using direct pronouns where indirect pronouns should be used -- it really gets me when the person speaking/writing is someone who has a degree related to writing, such as journalism or English.