Why, after decades of redesign and enhancement, does it still rain inside B737?
I've never heard of this on a 737. The last rows in a DC-9/MD-80 series is where I seen this the most.

The simplest solution is for the flight crew to set the cabin temperature control to not be full cold on a humid day. Just a little heat will cut down on the condensation being developed while sitting at the gate.

Here's an interesting article on moisture in the airplane, though it is not specific to the gasper vent rain. 

http://www.boeing.com/commercial/aeromagazine/aero_05/m/m01/index.html

Some larger aircraft have dehumidifiers, but as the Boeing article states


  Dehumidification systems (ground-based or onboard) are effective at removing moisture but are not cost effective.