Regardless of position, be the one who walks down the hall picking up tiny pieces of paper. Have teachers send a student into the halls at the beginning of each period to pick up the debris that falls out of lockers each passing period. Make each teacher responsible for the hall area in front of his room. Expect and inspect. A little organization can accomplish great things.
Teachers can do the cleaning, or they can have students do it in the last ten minutes of the day.
Have a scheduled inspection one day a week. Give each teacher a bottle of all-purpose spray cleaner to clean up spills or marks immediately. Have teachers check desks daily to observe and remove any marks. If a student doodles on a desk, that action should be treated as a serious offense. Hold quarterly locker inspections after school, checking for neatness and cleanliness.