Your rental is likely governed by WA Chapter 59.18 RCW (Residential landlord-tenant act) and the terms of your agreement that are not in conflict with the RLTA. The statutes are at http://apps.leg.wa.gov/RCW/default.aspx?cite=59.18 .
RCW 59.18.150 (Landlord's right of entry – Purposes – Searches by fire officials – Conditions) provides: "The tenant shall not unreasonably withhold consent to the landlord to enter the dwelling unit at a specified time where the landlord has given at least one day's notice of intent to enter to exhibit the dwelling unit to prospective or actual purchasers or tenants. A landlord shall not unreasonably interfere with a tenant's enjoyment of the rented dwelling unit by excessively exhibiting the dwelling unit."
Your contract may specify a longer notice period but not a shorter notice period.
While most people do not want strangers to see the people's homes in a mess, it is not your legal responsibility to keep the place in showroom condition. You can negotiate with the landlord for some compensation to keep the place looking nice. For example, he can hire landscapers to make the property looks nicer. Or, if you want to move out earlier, point out to the landlord that often it is easier to rent out a vacant unit than one that is occupied.
at least 24 hours. if he continues to ask you (while giving 24 hours notice), and it starts to interfere with your quiet enjoyment of the place - you should say something and negotiate either compensation or a scale back in the number of showings (i.e., limit it to one open house/week).