I am working on something similar... These answers are based on my limited knowledge. Please feel free to add/comment on my input.
1. Offsets are worse in CMOS because :
(a) MOS Offset is a function of threshold mismatch, which does not occur in BJTs.
(b) MOS Offset scales with overdrive voltage rather than Vt (26mV for BJTs), this is typically a larger value, in the hundreds of mV.
2. Your opamp's offset will be amplified, shifting your output DC level (error). Even if you compensate your curve, you reference voltage will be different from what you projected. Also, CMOS amplifier offset is itself temperature dependent, raising the temperature coefficient of the output voltage.
3. Look into "dynamic offset stablization techinques" using "feed-forward topologies" if you need continuous signal paths.