On Sat, 06 Sep 2014 16:22:14 -0400, Mr.E wrote:

Sounds as if the dishwasher "vent" is in reality an air gap that some
jurisdictions require.

I thought that. The air gap vent line is ordinarily attached to the
underside of the counter, with an arched loop. OP doesn't say if he
has a garbage disposal in the mix.

Pic:

http://www.fortworthinspector.com/sitebuilder/images/Air_gap2-646x335.jpg

https://tinyurl.com/nhl833v

OP is talking beyond the P-trap for the coupler leak.