when's the last time you lubed it?

I don't know how or why this is,.. but I can feel a difference in shifting after someone else has ridden my bike or driven my car...
It takes some time before things settle back to normal...

Try to make smooth shifts, and find the sweet spots of rpm and foot pressure...  Working with the machine will make shifts smoother over time...
Perhaps the previous owner was a brute and forced shifts instead of using feel...

... You might also check the shift lever adjustment... ...
You can't get all Yoda with yer' bike if it's got the controls positioned funky...
...
HINT (the shift rod is reverse threaded on one end)...


Trouble shifting at a stop, is normal... Bike tranny's don't like to shift at a stop...
If it won't engage at a stop... release the clutch and pull it in again...
This will jog the gear alignment and allow it to slip in gear easily...

Here is the order I would normally attack this with.   If the cable were sticky you would have jerky starts.  You can tell by letting the lever out slowly.  It should be smooth not notchy feeling.  From there check the cable adjustment.  Since your bike has 5K on it I doubt it is a break in issue.  My wife's S40 can be a pain if you are at a stop but I will cover that later.  If you find shifts are not smooth both up and down then you may have a miss-adjusted cable.  I had this on my sprint ST when I bought it.  The guy had aftermarket levers that didn't allow enough throw of the lever.  Check the lever while sitting parked.  do this when the engine is cold. (bike can be off)  You might have to pull the rubber boot off the threaded cable adjuster (up by the lever) if yours has one over it.   start to pull the lever just to the point the tension starts to pull back.  at that point you have taken all slack out of the cable.  Look at the gap between the lever and the perch.  it should be 1/8" or 3mm.  If not adjust it to that point.  If you have more than that what happens is you do not fully disengage the transmission with the clutch and shifts get notchy and clunky.  If that is all adjusted fine and it still does it up and down shifting while riding then you may have a bent shifter fork inside the tranny.  Lastly if it only does it when trying to shift while sitting still then that is not uncommon.  You may have to let the clutch out just a little and then pull it in again and try the shift again.  The transmissions have gears that slide sideways on the transmission shafts and drive dogs engage the gear next to it.  while rolling these mating parts are rotating slightly relative to each other and mesh smoothly.  When not rotating if they don't line up they don't want to go together.  That is why the slight letting out of the clutch and then back in many times works when sitting at a stop light as it moves the gears just enough to allow for alignment of the dogs.

Otherwise as mentioned if the shift lever is not adjusted right you don't get full motion of the lever before you hit the end of the motion of your ankle.  that can make for missed shifts and also the feeling of harder to shift.


Hope this helps

Regarding the clutch cable... I'd like to tighten it (I think), since the clutch point is so high/little pressure. But I can't seem to undo the nuts. In the picture, B&C seem to be linked, and I can't turn either/both of them and hold A so that things would be loosened or tightened. Given the moron that I am, what am I doing wrong?

New photo attached. The shifting isn't that I have to push really hard. It just is a bit more difficult (and crunchier, if that makes any sense).

Its 3 years old. Depending on where its been, how its been stored,, the cable could just need some TLC,, Dont disregard the advice of others, theres a ton of wisdom in their posts,, But,, I always try to start with the easiest answer, AND everyone knows that cables sometimes need a squirt,, Id pull the clutch lever in all the way with the cable exposed and put oil on the cable and if you can drizzle some in, great,, dont use WD40,, it evaporates and it will make it worse. I like the Zoom oil dispensers. I refill with 3 in One ,, or, there is a thinner oil, almost like sewing machine oil they sell,., Pull the tube out till it stops or it leaks.. or, get a squirt can or just a 3in one oil can,, AND,, you can buy a special gizmo that hooks onto a cable to allow you to Shove oil in, Ive never used one,, Look to see if its frayed, pull the ru bber back,, gonna hafta to oil it anyway..

From looking at your clutch cable picture where you were trying to adjust it down by the engine I would say that your cable is way too loose.  The head of the cable is stepped the smaller part of the head should stick up through the metal link on the main arm.  It isn't even showing.  So when you do make the adjustment make sure the smaller part of the head pilots into the metal link.  
See page 50 (by actual page number) of the user manual at this link
http://www.savageriders.com/verslagen/transfer/2002_LS650P_Owners_Manual.pdf

it will show you how to do the adjustments.  The one I described is the fine adjustment on the left, at the handlebar.  if you can't make up the difference there then you need to go to the right side of page 50 and do the coarse adjustment.

Likewise for adjusting the shifter lever you have a coarse adjustment by removing the bolt that goes through item A in your picture and move the lever one spline.  if that is too much adjustment or you want to make fine adjustments then go to the shaft that connects that lever to the lever your foot pushes on.  That shaft or rod has a lock nut on each end.  They can be loosened and the shaft can be rotated to make it longer or shorter to fine tune the foot lever position.  NOTE!!! ONE NUT IS RIGHT HANDED AND THE OTHER IS LEFT HANDED.

based the amount of cable play I see in your picture I think you are headed down the right track with getting the cable adjusted.