DIAGNOSIS The frosted plastic display on the Nest E is a smudge magnet. Using dry cloths, especially microfiber, can create static that actually attracts more dust, and oils from your skin or clothes just smear around.
FIX You need to break the oil down. 1) First, pop the display unit off its base by pulling it straight towards you. This lets you clean it safely away from the electrical connections. 2) Use a very slightly damp, soft, lint-free cloth (like a glasses cleaning cloth). Plain water is best. 3) Gently wipe the screen in a circular motion. 4) Immediately dry it thoroughly with a different dry, soft part of the cloth before reattaching it. Don't spray any liquid directly onto the thermostat.
IF THAT DIDN'T WORK For stubborn smudges, you can dampen the cloth with a tiny, tiny drop of mild dish soap diluted in water. Wipe gently and follow with a water-dampened cloth to remove any soap residue, then dry completely. Isopropyl alcohol is riskier as it can damage the frosted coating over time.
HEADS UP Never use window cleaners, abrasive cloths, or paper towels. The plastic scratches more easily than glass. Also, make sure the unit is completely dry before snapping it back onto the base—you don't want moisture seeping into the connectors.