Initial problem sounds like the damping system - shock absorbers at the bottom of the drum which are meant to minimize oscillations. Theyr'e two main types, either sliding pistons or a sprung friction pads which bear onto friction plates welded to the drum. Whichever type they are, they're probably worn out and needing replaced.
Drum problem - mmm..... Check out the carbon brushes in the motor. Theyre graphite blocks which transfer mains power to the copper segments of the motor - located at the other end of the motor from the drive pulley. Theyre probably worn down. They're quite cheap parts and easy to replace - the holders are plastic or bakelite and are generally held in with screws or plastic clips. Also, look at the copper segments they run on to check for burning or pitting. If the segments are burnt or damaged you need a replacement motor or a replacement armature (motor part) if you can source one. Occasionally may be a fault in the motor drive circuit board - in which case replacement of board only real option.
Spin problems may also be caused if the machine reckons the load is out of balance could possibly be a fault in the out of balance detector switch or the suspension and damping problem mentioned earlier
getting covers off...
unscrew screws at rear to slide off the top cover. check if there is a seam running down each side panel. pop small round circular plastic covers at the bottom, should reveal fixing screws. when removed machine splits in two. manufacturers are now using torx type screws to try to keep people out of the machines. you may need to buy a set of torx screwdriver bits to get the screws removed.
Check out my site for info: www.2ndwave.co.uk/manual.html
dan, February 2008