This is Herre förbarma dig (Lord have mercy) from a Catholic prayer book. The chords are D-D-D-G-Bm7-C-D7-G. V-V-V-I-iii7--IV--V7-I. iii7-IV feels a bit odd. We have contrary motion between outer voice which is good. Even parallel motion between the bass & tenor and between the alto & soprano. I don't even see how the Bm7 fits in the key of G, and usually a 7th chord is a major chord with an added 7th - not a minor chord with a 7th. What is going on?
I would call the Bm7 a passing chord in this context. It's purpose is to smooth out the transition from I to IV. The pitches in this chord are all in the form of passing tones that link chord tones.
The composer further indicates the passing nature of these chords by putting them on a weaker beat (all of the other chords occur squarely on the beat, while the Bm7 occurs on an upbeat).
So all together, this iiim7 chord is totally acceptable. It does not really serve a harmonic function, its purpose is to smooth out the voice leading from I to IV.
Lastly, minor chords can have sevenths (so can augmented, diminished, and suspended chords). The purpose of a seventh is too add some extra tension, so it is great for key changes, but it can be used in many other contexts as well. Minor seventh chords are extremely common in jazz.