As previously mentioned yours is a first series RS.. as Chaos has pointed out it has quite a few differences from the later 86 onwards model, from the fuel tank to the centre stand, from the instruments to the rear tail cowell. top to bottom, end to end, and many bits in between.
The later model , lets call it a Mk2... incorporated many design improvements in one swoop...having said that early versions like yours seem to survive perfectly well for 100,000 plus miles. The only concerning problem is that the centre stand is a bit weak and may collapse.
These bikes were styled by Hans Muth, The Suzuki Katana was also his work.
Most of your potential problems will be inside the fuel tank.. the aluminium tank can corrode if your unlucky. not a huge problem as pin hole leaks can be taken care off with a couple of blobs of epoxy. The fuel pump really suffers when the bike is not used. The old fuel degrades the rubber sleeve the pump sits in, it turns to slime and the pump ingests the mess and siezes. Man this can happen very quickly with fuel with alcohol in it.
It may look OK, try touching it to make sure its OK and not just semi dissolved paste. If all that is Ok and it cranks but doesn't start the injectors are probably frozen shut by dried out fuel resin. The in tank filter is Ok if you can "easily" blow through it. fuel lines in the tank must be suitable for constant fuel immersion ..if you need to replace make sure you get the right type. Remove fuel cap base (4 screws) to access tank insides.
The injectors will come out if you expose the fuel rail and lever it from each end with a small jemmy or large screwdriver. If it doesn't pop out with injectors attached, the injector O rings have gone hard.. squirt brake fluid or detergent at the base of each injector and try again. free the gummed up injectors with carb cleaner or acetone while running volts through them. Wash out tank with acetone if its contaminated..throw some objects in there like nuts and bolts and shake around.
The only other thing that I'm certain that will need attention is the headstem bearings. BMW choice of grease for these bearings was not a success. When left, the grease dries out and sets rock hard. Put the bike on the centre stand and if the bars feel stiff and notchy when turning the wheel lock to lock, drop the forks and get the triple clamps out and clean the bearings up and stick your favourite grease back in there. You'll need a 31mm or 32 mm socket and a lot of patience.
tell us what you find..