DIAGNOSIS You're right to be careful. That matte anti-glare coating on the Q80C can be damaged by harsh chemicals or abrasive cloths. Streaks or a hazy look after cleaning mean you used the wrong stuff.
FIX First, always turn the TV off and let it cool. Use a clean, dry, soft microfiber cloth—the kind you'd use for eyeglasses or a camera lens. Gently wipe in one direction, using light pressure. For fingerprints or smudges, barely dampen a corner of the cloth with distilled water (not tap water, to avoid mineral streaks). Wipe the area, then immediately dry it with the dry part of the cloth. Never spray liquid directly onto the screen.
IF THAT DIDN'T WORK For stubborn spots, you can use a tiny drop of isopropyl alcohol (70% or less) on the microfiber cloth, not the screen. Wipe gently. Avoid any cleaners with ammonia, vinegar, or abrasives, as they will permanently damage the anti-reflective coating.
HEADS UP Never use paper towels, kitchen sponges, window cleaner, or your shirt. The screen coating is softer than glass and will develop micro-scratches. If you see a permanent rainbow oil-slick effect after cleaning, the coating is damaged and can't be fixed.