The plumber just finished my kitchen sink installation, and I noticed that the horizontal pipe connecting the two sink bowl drains has a slight up-slope (maybe 1/8") over its length toward the point it "T"s into the trap. As I see it, there will always be a small amount of water puddled in the pipe because of this. To do it right, it should be sloped toward the trap. My question is: is this really a problem waiting to happen? Do I need to call him back to re-do the drain? Or am I just overly fussy?
I do not think you are overly fussy if you paid someone to install a drain line it should be done correctly. That said a drain to drain connector that was just a 1/8" difference would allow such a small amount of water to puddle in the pipe that it would evaporate in short order anyway.
Most of the piping pieces to make up a drain and trap assembly are typically joined with slip joints that can be easily adjusted. You may be able to simply move one or two joints slightly to correct the slope and avoid the aggravation of trying to re-engage with the plumber.