Let me start by pointing out that this quartet is obviously inferior to Haydn's op. 17 no. 3 quartet in E flat major. Ok, now that that is taken care of.
The first ten measures, in D minor, have these roman numerals
i IV64 ii042 i i V6 vii
IV6 Ger6 V V42 i ii V7 i
The device used in the cello part is a pedal tone. It is being used to prolong the harmony of V7/V. That's handy because the pedal tone is the root of that chord. Measures 22-29 are where Wolfgang falls for secondary dominants. It goes:
V7 V7/IV V7/vii V7/III V7/VI VI Ger6 V
This is a falling fifths sequence for a while. Wolfgang probably would not have gotten a good grade had he been in Spiegey's theory class, he hardly resolved anything correctly. In the first violin part the chordal seventh resolves up a seventh, then that leading tone resolves in the viola part, then the chordal seventh is resolved down a half step (yay) and everything is back to normal. In the second violin part the leading tone is resolved by the violist (cuz they know how to do it right), then the chordal seventh is right, but then the leading tone is resolved by the violist again (we have to do all the work). The violinists are playing in canon, started in the second violin part, with the second part a fourth up. It worked out into nice chromatic lines for both of them. How handy. Measures 30-39 are the same as the beginning, everything is the same as the beginning. He prolly just couldn't think of anything new. Or maybe he had somehwere to be.... we will never know. The end.