If there is a fault, it will generate a code imediately and it will stay in the ECU until it is cleared. That can be done with the OBD reader, should you get one.
The higher revs on starting from cold is normal and from what you have said, they settle down fairly quickly so that sounds like the injection system is working correctly. If she goes downhill on a closed throttle, i.e. foot right off the accelerator, is there still jerkiness?