I disagree and believe you should not use contractions in your PS. Every PS I have read from SDN has been wordy, so I am sure there are other options to shorten your PS besides using contractions. The PS is meant to convey your professionalism and maturity as well as your personality, and although people have certainly been interviewed/accepted with contractions in their PS, you don't know if there were schools that didn't interview them b/c the person pre-reviewing their app thought they didn't take the PS as seriously as they should have. To me it's stupid to take the risk, since it is unnecessary.
Try having someone else read the PS to help you shorten it. Almost always, applicants spend too much time describing things that aren't really relevant to the point they are making--if it's not about you and/or doesn't show your motivation, maturity, professionalism, etc., it can be cut down.
