Verified answer

Have you looked at the turn signal bulb AND bulbholder AND plug contacts? If bad contact is an issue, they would either appear:

Case 1 - "rusty" - oxidized

Case 2 - "melted" with some parts missing - caused by arching.

For case 1: Go to bavauto.com. They sell a product called DeoxIT.

This is not just a contact cleaner, it actually dissolves any oxidation found on the contacts.

This would solve your turn signal problem.

For case 2:

Option 1 - buy a new bulb/bulb holder (ie; whichever contacts are bad, change it out). For the bulb, the filament might look fine, but the soldered bottom contact might have a flat spot caused by heat from arching. Buy a new bulb (cheap) if this is the case.

Option 2 - you can try adding a conductive surface on yourself to get by (if the bulbholder base contact has melted some). If you do a good job, it could even last a long time.

You could solder a suitable material to whats left of the contact; or wrap some aluminium foil (a temporary solution only) carefully around the contact.

For your trunk, it is most likely an unrelated problem. Your actuator might be getting weak. Try some lube on the trunk catch (the part that moves). A weak actuator would still make noise when you try to open the trunk - even if it fails to open. Listen out for it. Eventually, you will need to change out the actuator if this is the problem.

BMWs (and most European cars in general) are notorious for electrical problems. I currently have a 2004 BMW X3 2.5i (purchased in May '04). Warning lights come on when nothing is wrong with the car and then sometimes won't come on when there is an actual problem, and the doors sometimes won't lock/unlock. My family also has a 2006 BMW 525i that has had similar problems. Ages ago in the early '90s, we had a 1989 735i that also had electrical problems, mostly with the power seats and windows. By comparison, we also have a 2003 Lexus LS430 that has had zero problems, electrically or mechanically (although it's definitely not as pretty or fun to drive as a BMW).

I recently had the same problem with my tail light. It was not the bulb but the housing that the buld fits in was loose and not making a conection. It you have a multi meter check or test light test the socket that the buld fits into.

The trunk, are you refering to the key fob not opening the truck or the switch in the passenger cabin?

The key fob may not work when dropped to often or the battery can get weak. Replace the battery and see if that gets better. As far as replacing the key fob you might as welll buy a new BMW.

The switch in the passenger cabin often the contact go bad and cleaning the contacts often helps. Again test the power at the switch in the trunk and the switch in the cabin. If you have a good repair manual it will help.

Best of luck.

the plug is rusty on the ground connection, wiggle or clean the contact at the rear of the plug

Look at the electrical circuit of your car...