Ultegra 6510 shifter broken - upgrade to 10 speed? My Ultegra 6510 9 speed right shifter broke. The screw holding shift lever to the back of the break lever popped out taking the threads with it. I don't know what the root cause of the problem but I was having issues shifting and I suspect that constant forcing while shifting on climbs likely caused the problem. I notice that the down shift lever is loose and wiggly and I suspect that the pin holding it place is becoming loose.

Now my issue is that the parts are obsolete. My bike is a Trek 5200 OCLV from circa 2002. Ultegra is now 11 speed, thus replacing it with a new Ultegra shifter is not possible without replacing the entire drive train and wheels, and I have a set Mavic Cosmic carbon wheels in addition to the stock wheels. Making an 11 speed upgrade not feasible.

The only new 9 speed shifter that I have seen is Shimano Sora 3500, but this seems to be major downgrade.

This leaves the option to upgrade to 10 speed. What will need to be changed? Obviously the rear dérailleur, cassette and chain. The chain rings will need to be changed regardless due to relative wear (new chain on partially worn rings). Is it possible to find 10 speed compatible chain-rings that will fit on an Ultegra 6510 crank? Or, is a whole new crank set required? Does the front dérailleur need to change?
Shimano groupsets get better over time so the latest R3000 Sora shifters are probably not as bad as you think. Certainly better than worn out Ultegra 6500 series.

You could upgrade to Tiagra 4700 10 speed, which again is probably actually better than the older Ultegra 6500. I test rode a couple bike with it and it seemed to comparable to the mix of Ultegra 6700 and 105 5700 I was running at the time.

I thought that 11 speed required a wider freehub body to accommodate the cassette, but I've read on this site that that is not always the case, so you might be able to go 11 speed.

About mixing and matching components: 

The difference between 9, 10 and 11 speed cranks is the spacing of the rings. Higher speed chains have a narrower outside width (inside with is the same) so the rings are slightly closer together. Opinion on this site seems to be that you can run a 10 speed rear and chain on a 9 speed crank without too many problems.

You can in fact run 10 speed rear shifters with a 10 speed cassette and 9 speed derailleur because Shimano 8, 9 and 10 speed road derailleurs do all use the same actuation ratio (except Tiagra 10 speed which used the 11 speed actuation ratio), so it you can find some used 10 speed Ultegra or 105 shifters in good shape those will work.

Unfortunately my knowledge stops at front derailleur compatibility, I've yet to figure out the actuation ratios for those.