For the Wembley show Bon Jovi hired a regisseur called David Mallett, who had worked with acts like Madonna, Tina Turner, U2 and Mick Jagger before, to shoot their concert. Initially it was even planned to release night one, but there they suffered huge sound problems while recording (meaning that some channels dropped throughout the show) and therefore they went with the final night.

About so many songs not making the final cut: Jon really put a lot of effort in it vocally when they started off, but his voice got shot during the show and he started to sound flat and weak on some songs. The radio recording shows that, Bed of Roses was quite boring and in my book they delivered one of the worst These Days performances as Jon couldn't go for the high notes at that point.
An indicator that the theory might be correct is that around 80% of the songs on the released video are from the first part of the show.
Although I also have no clue why songs like Runaway, Dry County, I'd Die For You or the classic jam with Bob Geldof didn't make it in the end as they all sounded pretty good. The only other explanation I can think of is the fact that it was released on VHS at that time and that it was a lot cheaper printing those shows to 90min video tapes instead of using 180min cassettes for the entire show.