A few very odd things have happened in the last few days:
1) On sunday I got gas and when I began to pull away the "Engine Control System" light came on and the car began pumping heat out the defroster full blast and the climate control screen went blank. "System Problem" was displayed on the DIC.
2) This evening on my way to work the car revved up to 1100 RPM's and began shaking badly in the front when idling and when moving with the brake off but the accelerator not being touched. then that pesky Engine control system light came on. The code I got was "B0030 - Right Front/Passenger Side Deployment Loop Short to Ground/Voltage Out of Range".
Both of these problems have only occured once.

Does anyone have an idea if these are related and what the problem(s) might be?

This may have been related to the bad battery you discussed in your other thread. Thse symptoms could be consistent with a low oltage sstem. Also you may have interpreted that code incorrectly - it is an airbag code and if memory serves MY 87 Cadillac did not have airbags :hmm:

Assuming all battery grounds are clean and secure as well as connections at the battery, You might check the "central power supply" module located under the dash just above the gas pedal. Remove the lower dash cover to access it. Mounts vertically and is held with 2 10mm nuts. Loosen the nuts and slide it off and down still connected. With the car running, slap the CPS with your open hand. Do the displays flicker? if so, check the connector to it. Shut off car and disconnect the harness to the CPS. Look for bent pins, deformed connectors in the harness plug. If all is OK, get a CPS from a wreck. They were famous for poor solder connections internally. Because this is an educated guess, do not buy a new one. Would have been nice to be referred by you to the other thread regarding battery connections. We are here to help, not be detectives.

If the CPS is found faulty make sure part number 16088406 is on the CPS. All other earlier part numbers are suspect. This part is used in Eldos as well as Sevilles.