If you have not yet given your tenant a 10-day notice to comply with lease terms you should consider doing that. Whether you did or not, you can send over a 48-hour notice of intent to enter and inspect. Best to serve it personally, but if necessary you can post and mail it. If you post and mail it, you have to allow one additional day.
The RLTA says landlords are responsible for maintenance and repairs. That' RCW 59 18 060. You cannot shift this obligation to the tenant even by contract. See RCW 59 18 230. If the tenant broke or damaged something, you can do the maintenance to fix it and then charge the tenant for the repairs. But you cannot reasonably expect your tenant to be your maintenance person.
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"What can I do or confirm that person move out or not?"
Doing an inspection is a good step for confirming the presence of the roommate. Look for obvious signs of more people living in the property than are authorized. If you know and can find the person who was living there, you could try confirming the person's address (a utility statement in his or her name is a good indicator of residence).
As previously commented, if there are unauthorized tenants you may be able to evict all of them, or at lease motivate your authorized tenant to get rid of the unauthorized roommate) by using the 10-day notice to comply or vacate. Refer to your lease agreement and seek the help of an attorney if you want to proceed with an eviction.
Also consider encouraging the unauthorized tenant to apply for tenancy rather than going through the cost of cleaning house. If they are otherwise a desirable tenant it may be beneficial to keep them.
"Can I gave 48 hours notice and go back to make sure the renter fix the issues?"
RCW 59.18.150 explains, and limits, the landlord's right to enter the property. http://apps.leg.wa.gov/rcw/default.aspx?cite=59.18.150 Read subsection (6) carefully on what must be done to exercise the right. The reasons for which a landlord can enter the property are quite broad and includes inspection of the property.
However, depending on what you mean by "fix couple of the items" and "fix the issues" you might not have the right to make these demands. It is very hard (practically it never happens) for a landlord to contract out of the duties assigned to him or her under RCW 59.18.060. Generally speaking, these duties relate to the maintenance of the property. RCW 59.18.130 lists the tenant's duties which include keeping the property clean and sanitary.