Electrical problems are more prone in the later Mk2 models due to them having a more complex wiring loom due to an ECU; however the older models still have their fair share of faults.
A common problem is the loss of the 12 volts at the coil and fuel pump. Although the pump is fed from pin 9 on the injection relay and coil from pin 1 they are both fed from the same source (internal link inside relay). The first relay will click in but the second will not. This is normally due to the relay not earthing through the ecu. The second reason for the loss of the 12volts is a plug underneath the ecu mount, these have a tendency to burn the contacts in the plug.
Be sure to check the crankshaft position sensor aswell on 92> cars sometimes they fail aswell
Rough idling can sometimes be traced back to the idle control valve (icv) in this case go to the scrappy and get another almost all Citroen's and Peugeot's have them.
Another cheap one to fix is the CO2 potentiometer (front of ecu cradle) if these throw a wobbler idle can be very poor sometimes non existent. This is only applicable on the pre cat gti's.
Post 93 cars have lambda probes in the exhaust downpipe and these can also lead to poor idling.
A simple way to check for miss firing is to have the engine running and to remove the lead to see if it effects the running of the engine, if it doesn't then you know that that cylinder is not firing. The AX runs on a wasted spark system so if 2 of your cylinders are not firing then you can assume that is is before the coil pack or the coil pack itself. On the GTI this fault is 90% of the time the Ignition amplifier which is located just at the back of the coil pack. If the engine is only missfiring on one cylinder it is probably the coilpack, HT lead or the plug itself.
Alternators have also proven to be a sticky problem for ax owners and will continue to be so. simple checks like checking the condition of the cable from the battery to starter and alternator will probably save breakdowns. Remember also check the neutral connection as this is very important!
70A alternator on TU engines will provide more reliability than the old 50A. These 70A are revised built and are upgraded for reliability.
Sometimes the rear lights can have faults where they fail to work, light up dim or light up the wrong bulb. This can ofter be traced back to corroded wires, the places to check are the plugs on the lights themselves and the wiring loom thats located behind the N/S Light.
Rewire a extra earth cable to the chassis where possible.