I recently removed the right side crankcase cover from my 78 DT125 to work on the clutch. When reinstalling the cover, I noticed that the cover wouldn't completely flush against the case. I frammed (safely) as much as I could but it wouldn't flush mount. I started to slowly install the screws and they pulled the cover flush against the case. I thought, problem solved! Then, when installing the kickstart, it wouldn't spring back up by itself. I removed the cover and checked everything, which seemed in order. The spring is where it is supposed to sit in the case. The stop is flush against the stop in the case, and the little spring that pokes out at the back of the starter is fit inside the hole at 12 o clock in the case. I then realized that the kickstart will spring back by itself when the case isn't screwed down. But, as soon as I torque down the screw that is right next to where the spring fits in the case, it stops springing back. I have no clue what is going on, but it sure is frustrating. Any ideas?

Are you using the factory thickness gasket?  

Also, there is a thin shim washer and a thick spacer that goes on the outside of the case...  thin washer, then thick spacer, then kick start lever on splines. 

I've seen people put the thin shim washer on shaft under the cover...  not correct.

www.cmsnl.com/yamaha-dt125-1978-usa_mode.../partslist/B-06.html
My guess is you've miss fired with #16 & have it sitting against the spring instead of over it--"see the small slot in plastic spacer". Tis interesting though looking at washer #17 but i guess it goes as it shows--on the outside to save the kick boss spacer from rubbing on the seal. Any chance you fitted that on the inside of the case as looking at the drawing it's thinner than the difference mis-aligning the thingy with a notch on the spring would make. MarkT? correct me please--if i'm wrong. Thanks.
Edit sorry i see Mark said similar re washer.

Thanks for the awesome help! This is why I come here! The issue did end up being the first part of your post RT. That big plastic spacer has a notch that fits over the spring and when the started mechanism popped out it slightly pulled back and turned, not allowing it to fully seat on the shaft. Problem solved! Works like new now. Thanks!