What is causing my kenmore 20702 washing machine to spin slowly during the spin cycle? Also has a clicking noise that happens when entering the spin cycle.

SOURCE: Kenmore Oasis Washing machine makes noise during Spin cycle

with the machine empty see if you can lift up only the tub and see if it drops down.check to make sure there is nothing between the tub and outer tub have you gotten an f-51 error?

SOURCE: Kenmore 80 Series washing machine - loud banging at end of spin

With the lid open, set the cycle to spin and press the lid switch button with a pen. Wait until the drum gets to full speed and release the lid switch. If the drum makes a knocking/ thumping noise and doesn't stop spinning within 2-3 seconds, the basket drive block is worn and needs to be replaced. (The basket drive block is located on the gearcase drive shaft, under the tub and agitator) If this has been happening for a long time you may need to replace the brake and drive tube assembly as well.

Basket drive block part number is 389140

If that's not it, let me know and I will try to help you further.
Good luck!

SOURCE: 22432 won't spin or drain

CHECK THE LID SWITCH THE PART THAT PUSHES THE SWITCH DOWN MAY BE WORN ENOUGH TO CAUSE THIS PROBLEM. WITH THE LID OPEN START THE WASHER IN THE SPIN CYCLE AND PUSH THE SWITCH WITH A POPSICKEL STICK AND SEE IF THIS PROBLEM STILL HAPPENS

SOURCE: Kenmore type 111, very weak spin

Clothes do not spin out good on NORMAL regular express, but do on casual.

SOURCE: Squeaking washing Machine during spin cycle

Hi
Loks that your machine is pretty old and hence the belt has hardened making a squeaking noise.
Good fix is get a new drive belt.
OR
Quick fix is you could put some oil on the drive belt..... it will work for now but not a permenant solution.
Regards
Berry