Josh,
Some benefits of the very popular three op-amps instrumentation amplifier (from W. Jung's book "Op Amp Applications"):
- common-mode errors in the input amplifiers tend to be cancelled out by the third amp (I guess this answers your original question)
- overall gain is being set by only one resistor
- this is a differential amplifier and common-mode signals are amplified by a factor of 1, regardless of gain
- CMR of this amp (in theory) increases in proportion to the gain
- large common-mode signals can be handled at any gain
Analog Devices and Burr-Brown (Texas Instruments) make those in a nice tiny packages with very accurately trimmed internal resistors.
Boris