Having given it a quick listen I'm not sure that the sheet music is totally correct, which doesn't help matters at all.
It feels to me like the B chord isn't really Bm, but rather it's more of a Bsus4 thing - there's frequently an E melody note over it in the instrumental sections. The bass also plays a fill that sounds distinctly major in character at one point.
So I'd think of it as being in E major, but nobody is really committing to playing the 3rd on the B chord, giving us I - bVII - V (or Vsus4, if you like).
The D major chord is a very common substitution, it's a borrowed chord from the parallel key of E minor and is labelled as 'flat 7 major'. This chord crops up all over the place, often with another borrowed chord (flat 6 major) before it.
Think about the turnaround of 'Crazy Little Thing Called Love', we're in D major, but we get Bb - C - D (bVI - bVII - I)
Totally agree on the first point, being able to actually play the thing takes top priority.
But... it's hard to 'learn the language' if you don't know what the words mean. A trained ear is a wonderful thing to have, but we need labels to put on the sounds we hear so we can categorise them - that, for me, is the value of theory.