ADC and internal noise
Things you can try to reduce ADC noise:


Stop the CPU during conversions. AVR allows this. I don't know if your dsPIC does.
Check noise on voltage reference (does it need a decoupling cap?)
Check grounding (if the part has an AGND pin)
Apply digital filtering (Increase sampling frequency not to lose too much phase margin)


And, yes, the lowest bits are usually noise.

If your dsPIC is part of a closed loop system, this will add noise to the output. However, since the noise is random, it will average itself out over time.