Question:

Why do many two-lane sections of some arterial streets, such as Harney and 30th, have dotted yellow lines in the middle as opposed to solid? I would surely think it's illegal for one to pass another vehicle on those streets, yet dotted yellow lines imply it is legal to pass other vehicles on two-lane highways as long as there is no oncoming traffic.

Answer:

Passing is only allowed if it can be accomplished safely and speeds are not exceeded.  According to the striping passing is allowed.  The dashed line allow cars to pass if they can follow the rules of the road.  The road is not a 65 mph highway though.  In reality it is very difficult to pass a vehicle on these roads safely and not exceeding the speed limit.  It would more be used for passing if a vehicle was traveling very slowly for some reason or stopped.  
 
As noted in the Wyoming Driving Manual, yellow lines separate traffic flowing in opposite directions and broken lines indicate passing or lane changing is permitted if the way is clear.