Toilet keeps running

After doing some more research, I answered my own question. Fluidmaster is very deceptive in its claim that their 400A valve "fits" both 1-piece and 2 piece toilets. Yes, it "fits" BUT IT DOES NOT WORK THE WAY IT IS SUPPOSED TO! One piece, low-profile toilets have the tank water level below the rim of the bowl and require a special diverter valve that initially directs water to the rim when the flapper is open and then switches to filling the bowl when it is closed. If anyone is interested, I just ordered one (the LASCO 04-4165 Coast 1B1X) for $22.50 from Amazon.

If your tank is constantly leaking water, but you've not found it anywhere, then it is nigh on certain that it's going into the toilet bowl. Tester101's tip of putting food colouring into the tank and seeing if it appears in the bowl will likely confirm this.

The issue is then to find exactly where the leak is. Either your flapper isn't closing properly, there's a leaky joint where the overflow pipe connects (just below the flapper), or the seal between the flapper apparatus and the tank isn't watertight.

I would hazard a guess at it being the seal between the flapper apparatus and the tank, probably due to either under-tightening or over-tightening when installing the new flush. Over-tightening is perhaps the more likely - it shouldn't be tightened too much or you will distort the rubber seal.