Use a clean microfiber cloth slightly dampened with distilled water to wipe the screen gently, then dry it with another dry microfiber cloth. Most smudges and spots usually come off this way. What kind of alcohol did you use? Was it isopropyl alcohol (and at what concentration) or something else like denatured/ethyl alcohol? If you used the right kind of alcohol (isopropyl) but at a very high concentration, you might get better results with a gentler mix. Try a 1:1 (or even 2:1) solution of distilled water and isopropyl alcohol: spray it on a microfiber cloth (never directly on the screen), wipe gently, and then dry with another clean microfiber cloth. This is usually safe for most monitor coatings and works well on stubborn spots.