I'm not quite sure why that 3/4 time traditional Whomp-chew-chew beat doesn't seem to fit. The Eagles were doing a Western Country-Rock thing with Desperado and certainly that waltz beat is a HUGE part of that music. It is used a lot in that particular genre. I think it may be because the rest of the songs have such a more contemporary beat.
Now, I've messed with a lot of music based on 3/4...Take "House Of The Rising Sun" as an example...it isn't 3/4 but it is based on it....6/8 actually. If anyone has trouble "hearing" what I'm talking about, Sing the Church Hymn "Amazing Grace" but sing it to the tune of House of the Rising Sun. It fits that beat perfectly...like a glove. But the Original Amazing Grace is 3/4 waltz beat and that is what Saturday Night is.
Now, I'm quite sure that when arranging that song, Glenn (I assume that Glenn wrote it and arranged it) had some reason for keeping it in that beat instead of kicking it up to 6/8 which would have meshed into the rest of the beats on "Desperado" much better.
But that is MY TAKE on it. And believe me, I have nothing But Respect for the talent that Glenn has for arranging music. Henley may have the corner on lyrics, but it is Glenn who pulls it all together into a unified whole. Maybe Glenn was still discovering himself in those early years. OR maybe he accomplished exactly what he was after, but it sure made Saturday Night sort of stand away from the rest of the songs on the released album.