The inertia switch trips in the event of an accident and presumably stays tripped until it is manually reset (which requires removing the lower passenger-side kick panel to access the switch. When the inertia switch trips, power to the ignition and fuel pump is interrupted and a signal is provided to automatically unlock the doors.
If your car still runs, then the inertia switch did not trip; however, it is possible that you may have a loose wire or intermittent connection in the inertia switch signal to the ECM such that the ECM "thinks" the switch has tripped, which causes the ECM to start the "flight data recorder" and store a code P1582 which indicates that data has been recorded. I would think the data that was recorded should include exactly what event triggered the recording (i.e., inertia switch trip, engine stumble, engine stall, etc). Bottom line is the Jag dealer should be able to read the transient event recorder log and tell you what caused the trip as well as a bunch of other potentially useful (or maybe useless) information, like how fast you were going when the event occurred.
Before buying a new o2 sensor, I would recommend reading the codes again to see if the same three codes appear. I can't think of anything that could tie the P0037 and P1582 codes together. Also, the O2 heater circuit is pretty easy to troubleshoot. If you ultimately decide to buy a new sensor, shop around. Here's one link....http://oxygensensors.com/index.php?r...FRBM5Qod0SovLg
Just fill in the requested model info.
I can't find the P2503 code in JTIS. Sorry.