Hi
> PDC light flashing
Suggest diagnosis via ODB/DLC to ascertain fault.
> Satnav - No menu
Not quite sure what you mean here, does the button not work, or what?
> CD Changer fault
Ebay is your friend here. They go wrong quite a bit! I think from memory they go for around £40.
> TV fuzzy picture
It's an analogue TV and analogue has been switched off in the UK.
> Rear door card loose
Probably means someone has had it off for a window lift mechanism and broke the clips!
> Rear right speaker fault
Probably not re-assembled correctly.
> Rear right window film scratched
Probably whilst removing the glass to do the window regulator!
> Gear selector not synchronised with dash
OK, there is a strange electical switch thing that's screwed to the gearbox selector shaft and tells the car what gear it's in rather than what gear it thinks it's in. They corrode and go wrong and are horribly expensive from BMW. But you need ODB diagnosis to confirm and you should get TRANS PROG FAIL messages if it's that unit. I managed to find another cheaper source for the exact same part when it failed on mine, if it turns out to be that unit let me know and I'll dig out the details for you.
> Fuel gauge not accurate
I think this has been covered elsewhere.
> Wing mirror light loose
Not sure, I think I'd be tempted to bond it in place carefully if everything else about the mirror is good.
> Vibrating noise from cold engine
Difficult to diagnose remotely.

Re: independents, we have a fairly good one here in Newbury which isn't a million miles from you, but I expect you can find a more local one.

If you come down this way let me know and I'll do what I can to help. However please note I'm away all next week.