I am just getting started with Arduino and electronics, so I can't speak much about circuits, but I work for a digital scale company and have too much knowledge about scales. Here are some links that might help:
http://www.weighing-systems.com/TechnologyCentre/Strain1.pdf
Fundamentals of Weighing Technology - Attached. EDIT: Arduino forum attachment isn't working. When I download the attachment, I only get a partial file that is corrupted. Sorry.
There are many sources of error in weighing systems that get filtered out through hardware and software. Besides internal electrical noise, there are also errors from things like load cell hysteresis, vibration, temperature fluctuations, etc. Most digital bathroom scales also adjust the zero point each time they are turned on, and aren't meant to be left on constantly. Digital bathroom scales typically use four cheap steel loadcells which aren't the best for high accuracy, but do well in home use scales. More accurate platform scales will use one single-point load cell, but they cost quite a bit more than home bathroom scales and aren't as low-profile.