titch-- yes, clean the pivots.
Also, remove the two wee phillips screws that hold the aluminum plate on the body.
Under that aluminum plate is a square of agate with a "V" cut into it that the pivots rest in.
Clean them up too. Use an alcohol wipe and get any gunk off of it.
Make sure it is dry, no oil or anything.
mlehto, any beam will work. Almost any of them will be more user friendly than the Lee.
I have an ancient Redding oil dampened, and even it settles down quickly, but I "help" it with my finger.
My Bonanza is all plastic, and so sensitive that I have to be careful to direct my breath away from it.
They both agree with my Lee, and I trust any one of them more than my Hornady digital.
Put a weight on the digital and let it sit a moment and watch the reading get heavier.
Weigh something, take it off and immediately put it back on. Now the reading is off by 0.3gr.
I'm not going to throw it out, it is handy to find the weight of something, but not for trickling.
Trust but verify
A beam can be pretty quick to use, but the Lee could make someone lose their patience with it
before they ever got proficient with it. I'm sure you could find someothing inexpensive in the EE
if you don't want to spring for a new one.