First, a link to the song reference in the title: https://www.youtube.com/watch?v=T4bkE9s_jy8 (from The Music Man)

Now, Rivet City (instead of River City, per Music Man) is giving me headaches. It started when I was trying to find a way into the broken bow section. I exited outside onto the upper deck and could, for the life of me save a game (quicksave or hard save). The game crashed every friggin' time! Well, I continued on and prayed I would not die. I made it through and eventually was able to save my progress once again.

Now, I loaded down and nearing Rivet City again, with The Jefferson Memorial off to my right. I can save in a "plaza" area where I have dropped off my loot. Then, I come across a Mutant fortification with a prisoner. I have cleaned out this area 15 times! I can not save just before it, nor after it. I can not even get to Rivet City before the game crashes and I am back, doing this all over again.

I know I have not given any PC hardware info, but is this a common thing? I am using the unofficial patches (all DLCs). I am also getting VERY frustrated!

I don't know if it's common (I've only been playing since October) but I've never had any difficulties saving in that area. For the record, I don't have the Unofficial patches. But I can't imagine that the Unofficial patches would cause problems. I hope you get this figured out!

By the way, I love your Music Man reference. Years ago I played Marian, the librarian in a high school production. It was not up to Broadway standards (or off-Broadway) but it was very fun.

This is why. There's a bug with one of the unofficial patches that causes the crashes. IIRC, it's the one for Broken Steel. There's an xmarker the patch has left in that was removed in the official Broken Steel expansion. That conflict causes the game to crash anytime you try to save in that area. I was able to find and remove it using FO3Edit, but I believe there's also a fix available somewhere on the Nexus.