Many parts of the Ring Road have no streetlights, and can have sharp turns and curves so drive accordingly
Watch out for sheep or other wildlife crossing the Ring Road
Download an offline map of Iceland in Google Maps as well as Maps.me. Sometimes Google Maps won't have as complete a map, so it's good to have a backup. Maps.me also does a good job of showing some walking trails.
Bookmark washrooms and gas stations along your planned driving route. The further out you are from Reykjavik, they can be few and far between.
Beware of speed cameras! You will rarely see police or traffic cops out because most areas are quite remote. Some speed cameras are marked, you will see a street sign with a camera icon leading up to the speed camera. Fines can be very high! Speeding tickets can also be sent to the car rental company, who will forward the fines on to you by mail.
The Ring Road is only one lane in each direction and generally well paved.