The only minor irritations I've had over the years have been:
I never tried running larger bulbs on the standard wiring loom and switch, but I know someone who tried an experiment on another type of car, and couldn't tell the difference because the standard wiring just lost so much power. And someone else I know found that their headlight switch melted, and then they had nothing at all - not fun (I was there at the time...).
I made a completely separate wiring loom for my headlights. To save cutting the standard loom around, I've actually left the original headlight wiring in place, and removed the fuses. Triggers to the relays are taken from the original fuse holders (clean them up with some flux before trying to solder to them, it works wonders!). Power feeds to the relays are taken directly from a power distribution point adjacent to the cut out switch or battery. Use wiring which will cope: if you are running two 100w bulbs through one relay, 17A cable is only just able to cope. I used something around 30A cable from the power feed to the relay, and on to the additional fuses (one per filament). Beyond the fuses, the 17A cable is happy with the 9A load from a single 100w filament.
A similar process is used for the auxiliary lights. Dont forget that the relay trigger for spot or driving lamps must come from the main beam circuit, and the feed for fog lights must come from the sidelights circuit, in order to be road legal for the UK. It is always worth having a separate kill switch for auxiliary lights of any sort, as events (especially road rallies) will often have sections of route where auxiliary lights are not permitted.
Charging System
If you are running any sort of serious lighting system, you will find that the standard (37 amp) alternator is just not up to the job.
There are a number of options for uprating the alternator. A 55 amp alternator from a Ford XR3 is one common option, which is not a lot more than the standard item. Another option is to find a friendly auto electrical outlet who can build an alternator to suit.
A 55 amp alternator is all well and good, and seems to run 400 watts quite happily, but watch out for the alternator loom. Even pushing a 55 amp alternator to its limits is probably too much for the standard loom. The best solution here is to replace the standard loom, from between the starter and the alternator, with uprated cabling - two 60amp cables fits quite nicely into the both the connector and plastic 13mm I/D conduit. Where possible, it's probably best to run them straight to whereever you distribute the power to the big loads - either the back of the cut-out switch or the feed to the relays.
I've never had problems with overheating alternators on Sunbeams like you get with many cars, but I have seen several occasions where the regulator has physically broken inside the alternator. There's not a lot you can do about this, unfortunately. The only other way I've killed alternators is by dunking them in deep fords, but that's kind of unavoidable really.
Starting System
The starter motor and feeds to it on the Sunbeam are nothing out of the ordinary. However, when you are using the standard ignition system, I have seen problems when using starter motors which don't have the plethora of extra terminals that the Talbot/Chrysler ones have. Generally, you end up with a no start condition but sometimes I have seen conditions where it will only fire while the starter is running. It's all to do with the ballast resistor bypass circuit, and I've never really sussed out why. I used to put up with the additional cost of getting the correct starter motor, but now I've replaced the ignition system with one which doesn't require a ballast resistor.
I've never had any heat related starter problems, the only problems I've had have been related to age of the starter, and possibly a bit of water ingress causing the solenoid to sieze.
Ignition System
The ignition system was state of the art when the car went into production. A hall effect sensor in the distributor meant no problems with points gaps etc. and a reduced spark voltage for less battery drain. A solid state amplifier took the signals from the distributor and provided the coil drive in one simple unit.
I've never had any problems with the standard system. Coils wear out, but then again they do on any system. The ballast resistor can get a bit manky, especially given its location, but beyond that there's not a lot to go wrong.
But by modern standards, the coil voltage produced by the system is quite low. Some of this stems from the use of the ballast resistor deliberately reducing coil power, and some of it stems from the fact that electronics have come a long way in the last twenty five years or so. Upgrading the ignition system, or even replacing it with a mapped system, is something which many people will want to do to extract those last few horses from their engine.
The standard system can be removed by unplugging its loom from the connector at the bottom of the offside inner wing, near the crossmember. This is a very neat and tidy way of removing all the wiring associated with the standard ignition system.
What system you choose to use is up to you, and probably depends on how serious you want to get. At present, I'm using a Ford system (probably from a Mk4 Escort of some description). It's a much smaller unit, and does away with the ballast resistor as well. The additional spark strength means you can open the plug gaps out to 40thou. The parts are marked as follows:
A word of note: If you do fit an aftermarket ignition amplifier, or even just rewire the existing one, be very very certain to check the ignition timing afterwards. Simply swapping the pickup wires shifts the timing some 20 degrees or so, and the first you'll know about it is when you find a hole in your piston...