Whose job is it to keep the sidewalks clear of vegetation?

It is your job if you are the property owner or manager!  RCW 35.21.310 Removal of overhanging or obstructing vegetation — Removal, destroying debris; "The ordinance may provide that if such removal or destruction (of vegetation) is not made by the owner after notice given as required by the ordinance in any of the above cases, that the city or town will cause the removal or destruction thereof and may also provide that the cost to the city or town shall become a charge against the owner of the property and a lien against the property."  This code allows each city or municipality to form their own code and enforce it.  Every city has an "owner must clear right-of-way code."  Check on-line or at the library to find out what applies to your area.

By Washington State  Law, RCW 17.10.140, invasive or noxious weeds listed by the Washington State Noxious Weed Control Board must be removed or controlled.

Knotweed, Blackberry and Scotch Broom are peaking and should be cut back if it hasn't been done already.  Check with your Washington State Noxious Weed Control Board for the top 50 invasive species list for methods of control and removal.

There are many reputable companies that practice sound IPM (Integrated Pest Management) and (IVM) Integrated Vegetation Management that can help you out.

If you are interested in getting more involved with vegetation management in Snohomish County there is a program called VegMon Snohomish County Surface Water Management you can participate in call 425-388-3464 and ask for the Vegetation Monitoring Program.