[exray]

Secondly, although I'm now getting stations more accurately in the right places, I notice a tuning 'whistle' just as I tune into a station. When it's tuned in, all is well - so it's not really a big deal - but it was not there before.

That's a symptom of oscillation in the IF amp stage. I'm assuming that the radio has been recapped? Sometimes physical placement of the caps, missing tube shields, poor grounds via rivets can cause this. A last-ditch band-aid is to detune the IF transformers slightly so that the oscillation stops.