Don't avoid 'pseudo-intellectualism'. Libbsters example of this was in fact, a cliche combined with a phrase that is meaningless. She wrote a useless sentence.
Take great care in developing an argument, and identifying your premises. Take consideration of the chief objections to your view, and incorporate this into your argument. It will make your essay look stronger if you show that you understand what the contested parts of your argument are.
Clarity and concision are the two goals you should be aiming for with your writing style. It involves a lot of work, but make sure that every word you write means exactly what you think it means eg most definite. What is the use of most in this context? It is either definite or it is not. Write with a dictionary next to you (or use the Oxford online dictionary). NEVER use words you think are intelligent, more often than not it makes you look like a moron (cf Libbster). Read, and re-read, what you have written multiple times. Learn to draft, making sure that each time you read through you identify the parts of your essay that don't flow properly. Concision means you should always write using the least amount of words necessary.
George Orwell said:
Consider for instance some comfortable English professor defending Russian totalitarianism. He cannot say outright, "I believe in killing off your opponents when you can get good results by doing so." Probably, therefore, he will say something like this: "While freely conceding that the Soviet regime exhibits certain features which the humanitarian may be inclined to deplore, we must, I think, agree that a certain curtailment of the right to political opposition is an unavoidable concomitant of transitional periods, and that the rigors which the Russian people have been called upon to undergo have been amply justified in the sphere of concrete achievement."
Always be sincere in what you are arguing. People may claim that bias will mark you lower, but in reality that doesn't occur. I received HD marks on essays where the lecturer is Marxist but I am a libertarian/conservative. When you aren't sincere in what you are saying you tend to qualify every statement you make. This destroys any argument you are attempting to make. Say what you mean, and mean what you say.
Good guides to writing essays or writing in general:
Oshima & Hogue, Writing Academic English
Fowler's Guide to Modern English Usage (Highly recommended)
Robert Graves, The Reader Over Your Shoulder
Orwell, Politics and the English Language
http://www.mtholyoke.edu/acad/intrel/orwell46.htm