Two mistakes I see writers make a lot are switching verb tense and point of view. Let’s take one at a time.
Verb tense consistency means that whatever tense (past, present, or future) you are writing in, you should stick with that consistently throughout the essay (or article or novel). Obviously, there will be times where it’s appropriate to change, such as in a flashback or thoughts about the future. Many times, beginning writers start out in the past tense, then randomly toss in present-tense verbs (or vice versa). You can catch this by, when you’ve finished writing the piece, going through and highlighting all the verbs. Unless it’s a clear case of needing to switch for a flashback, make them all the same tense.
The other inconsistency that I see a lot is changing point of view. Often beginning writers will start out in first person (I did this or that), then inexplicably switch to second person (you did this or that). Again, this is a problem that is easily fixed with careful editing: highlight all the subjects of your sentences. Obviously, you can write in first-person essay and still have a second-person subject in some sentences, but unless you are writing a how-to guide (such as this one), you shouldn’t have “you” as a subject.