Floating Rear Brake maintenance is commonly overlooked and can have a severe impact on a bikes suspension and handling. This type of rear brake was common up through the 80s on both dirt and street/road race bikes.
Now you might be thinking, "How would this backing plate have any effect on a bikes suspension or handling?"
Well, since the brake "floats" it moves with respect to the rear axle as the suspension moves. This means that any binding in the backing plate bushing, or stay arm pivots will inhibit suspension movement. This has a huge effect on both traction and harshness! This means that even the best suspension will work poorly when there is drag.
The main culprit is usually the Backing Plate Bushing itself. This is between the rear axle and the backing plate. These can bind for one of two reasons; first is simply neglect. The bushing is dry and/or corroded. Second, sometimes the dust cap on the outside of the backing plate on the axle gets grooves in it (over-tightening the rear axle or long-term wear) so when the axle is tightened it no longer has clearance.
Maintenance is pretty straight-forward; clean, inspect, grease. On the other hand if the dust cap is grooved you will either need to replace it or figure out a way to get the clearance back.
Next check the bearings at both ends of the stay-arm. These are all pretty simple; either spherical ball bearings, needle bearings or plain bushings. Take them apart, inspect them, replace if needed and grease 'em up.
You should be able to freely spin the backing plate with the rear axle tight and the stay-arm off. This is commonly overlooked and can reap huge rewards with a little love.