A CE680 flight crew experienced multiple failures on approach apparently related to Air Data Computer issues.

Narrative

On the arrival into ZZZ; we had deviated around a line of weather in vicinity of ZZZ1. This caused us to delay our descent to clear the tops of the weather. After we cleared the weather in and around the intersection; we started a descent to cross ABC at 11;000 FT; 250 KTS. We had both the engine and wing anti-ice on prior to descent and it was all operating normally. Descending out of FL240; we entered an area of light precipitation; no convective weather was shown on the radar; just a large area of light returns. The aircraft in front of us on the arrival reported light to moderate chop; but it was not too bad. Right after we entered the precipitation; we got the wing-anti cold left; followed in short order by the engine anti-cold left and wing anti-cold right messages. We increased the power and added speed to keep our descent rate up. The messages all cleared in less than 1 minute. Descending through approximately FL210; we received an Engine Control Fault Left/Right message and also at the same time an Autopilot A/B Fail and Yaw Damper A/B Fail message. The pilot in the left seat started hand flying while I troubleshot the problem. We tried to reset the autopilot with no success. I was starting to get the checklist for the engine control fault message; when the pressurization spiked to 4;000 FPM descent. I was able to slow the cabin to normal by going to manual mode. The cabin was showing 1;000 FT below sea level; with a differential of 4-5 PSI (well within the normal range). During this time we were in light to moderate precipitation with very light turbulence. The next fault was a comparator warning for IAS. I went to the checklist for that and troubleshot the problems to the right seat Indicated Airspeed Display. The checklist was followed and system reverted to ADC 1. Next; I went to the Engine Control Fault checklist and was not able to get the system reset per the checklist. That fault did clear on its own at 8;000 FT. The pilot did a good job of aircraft control while I ran the checklist and sorted out the multiple faults. Due to the gusty winds and wet runways; I elected to make the landing which was normal. The airspeed fault and autopilot faults did not clear until after landing. We wrote up the multiple failures after landing. Overall; the event went smoothly; but in talking to other pilots afterward; I heard that similar events before were linked to an ADC failure. If this is the case; it would be nice to have the information; so when it happens; we are more prepared. Clearly; the failure could have been caused by something else as well.