The person you choose to look over your statement should be checking everything. Along with grammar and spelling errors they should check the tone of the paper, the flow of the paper, and the overall style of the paper. So, it makes sense that the person you choose to look over your admission essay should be well tuned in writing. Additionally, they should also be able to let you know if there is anything they feel you should omit or add. Once you have made the changes they recommend, then you should have them re_read your personal statement to ensure quality. If you want to be ultra_safe, then have yet another set of fresh eyeballs look over your revised personal statement.
After grammar and spelling, the next problem that needs be checked is transition. Read your essay. Go through it from end to end, and check to see if your essay flows smoothly. Does each sentence flow smoothly to the next? Does each paragraph flow logically to the next? Each statement should be connected or somehow related to the one before it, not thrown randomly together. Next, limit the use of "I" in the beginning of most sentences as it is already obvious that the essay is a piece written by an individual.