Exceptions to rules for matching chords to melody notes

The song starts with the refrain in key of D major. In the verses it switched to Bm. I saw that right away since the first 3 notes in the 1st measure of the verse were Bs where the refrain started and ended on D.

What really threw me was the verse ends on the note E but the chord provided was a G! Since this note was the last note of the song and was not a passing note, it needs a chord. What logic would I use to come up with a G Major chord?

The mini-course I took stated that the chord should have the melody note in it. What other "rules" do I need to consider as I practice putting chords to songs with only the melody?

The chord probably should have been a G6 which is G,B,D,E.

Two things. The first has already been discussed - the melody note will be harmonized if the chord played under it contains some of the melody notes in it's makeup. This chart will help:

1 degree of the scale try I, IV, vi or ii7 chords of that key.
2 degree of the scale try V, ii7, iii7 chords of that key.
3 degree of the scale try I, vi, iii chords of that key.
4 degree of the scale try IV, ii, v7 chords of that key.
5 degree of the scale try V, I, iii chords of that key.
6 degree of the scale try IV, ii, vi chords of that key.
7 degree of the scale try V7, iii, Imaj7 chords of that key

And then it's a balancing act between harmonizing the melody line and having the chords move the progression along on the rest, tension, climax, resolution and back to rest journey. The classic I-IV-V-I achieves this very well. Trick is to balance both - move the progression and harmonize the melody line all at the same time. As the I-IV-V chords of a key contain every scale note in that key you can get by with just those three chords.

However, as bitcomm mentioned extensions play into this quite well.

Using that chart you could have a chord for every melody note - bad idea - insert a new chord when the melody moves on to notes not found in the old chard, i.e. your ear will tell you that something is not harmonizing -- then it's time to find another chord.

One thing I learned, no matter what the rules say, if it's sounds good, you're ok.