Yes. And the small electrolytics too. The zener may be bad, but likely as a result of a major failure of another component. Zeners don't just fail due to old age. On the other hand, electrolytic capacitors only last so long. After about 10-15 years, they are a ticking time bomb. Your scope is 40 years old. Best to replace all electrolytics near ground zero of the bad zener, and then plan to re-cap the whole thing in the near future.
Coincidentally, I'm in the process of recapping my own 30 year old scope, because of erratic behaviour.