It's ages when I was at the school and we were playing with A/D circuits, but if I recall right, few points in random order:
* Digital system requires different "good" power supply than analog system. You want pretty exact voltage level and rigid power line i.e. aux. supply capacitor for each circuit and near IC:s that cause surges.
* Analog system requires it's own power line/filtering and same on return line.
* Shielding and grounding must be kept separate. Grounds connected only on one point on chassis.
* ADC supply and signal lines must be considered carefully, Best to shield it too and sow ferrite beads on every analog/power line out. Best to tuck the whole cacadoodle on outside corner of the PC board as far away from processors and their fast busses as possible.
Much of the problems comes from noise that is introduced to power feeds....Circuit board could be right, but all wires tied to same bundle and grounded randomly....
Some of the stuff here sounds familiar(ish):http://www.analog.com/library/analogDialogue/Anniversary/12.html
Designer might have made some choices allready.
When I don't know what to do with grounds that are connected less than ideal way, I'll toss small resistor in series towards to "dirty system" and ferrite bead over the wire/leg. There will be small voltage drop, but on analog system that hardly never matters and even on digital systems you'll get away of it if you have decent coupling capacitors on IC:s.
This sort of idea:http://e2e.ti.com/cfs-file/__key/CommunityServer-Discussions-Components-Files/64/8371.Audio_5F00_ground_5F00_isolation.png
There are finer points on ferrite beads, but I don't have need to go there:http://www.sigcon.com/Pubs/edn/ferritebeads.htm
Only thing I know that this concept has got me out of pickle, maybe basic understanding of the problem and token beads were just enough for me to avoid bigger problems.