this is quite a hard song to play because it is very slow. It's probably only 50bpm. Coupled with simply one of the best vocalists ever it makes any error in timing near catastrophic. Sadly I have never been lucky enough to be in a band with this tune in it's repertoire.
key = probably A major

but it has a F major chord in bar 8
this tune (like our favorite , Maxine) modulates up a semi tone, to Bb in bar 26.
is it possible the F major softens our ears for this change? who can say, weird or what as Shatner told me in the news break.
there are 2 x12 bar progressions;
A / E / A / E / A / C# minor / D / F major / A / E / A / E /
followed by
A / E / A / E7???? / A / C#m / D / F major / A / E / A / F major /
then the outro which is
Bb / F / Bb / Gb maj /
it just repeats the Bb to Gb thing to finish
what is Bb to Gb? it is a minor 6th.
what is Gb to Bb? it is a major 3rd
make of this what you will I'm unconvinced I know exactly what point it is (if any) I am trying to make.