Here's the first mistake, although it is not necessarily the most common mistake or the most important one:
Failure to restate the topic
See a lot of essays that start like this:
Yes, I agree wholeheartedly with this point. It is very important issue, and I agree with it for several important reasons.
Can you figure out why this essay introduction is not good? This sounds pretty good and the grammar is good. But what's wrong with it?
• This introduction is not good for the TOEFL because it does not introduce the reader to the topic. Otherwise, after we read this introduction, we are not sure what the essay is going to be about.
• The person who writes an essay introductoin like this is probably thinking that the reader already knows the essay prompt (the "question" or topic of the essay) and doesn't think that she needs to restate the topic.
• For the TOEFL essay, it is most certainly true that the reader of your essay does know what the essay prompt is, but the TOEFL test taker must still introduce the topic of the essay in the introduction.
• The rule of thumb in English (our English teachers tell us this over and over) is that we should write the essay as if the reader had no previous knowledge of the topic we are writing about. It means that you should be sure to restate the essay prompt (it's best to paraphrase the prompt, not copy it word for word) and to explain the things in the essay that the average reader would not know about.