Problem 1: Look at the picture that I've included. I'm sure someone with any kind of experience will recognize this problem right off the bat. Does the screen need to be degaused or something? If it's permenant, oh well, it's still a sweet deal!
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The problem with repairing oscilloscopes is that you need another scope (with a HV probe) for your trubleshooting. The Tectronics manual is a must after you have looked for any obvious signs of damage, they are expensive, check Ebay for a used one or Googel for a dealer in used test equipment.
Questions, is the distortion very much the same on all sweep freq's. The focus of the trace is not great in the picture. Could you post another picture with about one cycle per cm. Is the focus knob about in the center? I dont think the CRT could be dammaged to cause that type of sweep, you might have some fluxiation in the HV powersupply or the sweep amps.