Yep, I know about plumbing problems living in a 60 year home myself! Over the past few years, I have had to replace all the drain pipes with new PVC stuff. That cast iron stuff really cloggs up when it gets old!
I experienced the first drain backup the day I moved into the house, which was on Superbowl weekend. After spending the previous few days moving, I had all my friends over for the Superbowl, and we cooked up a serious feast! That serious feast amounted up to a serious load of dirty dishes! My friends were rinsing off the dishes and putting them in the dishwasher. Little did we know that the mess being washed down the disposer in the kitchen sink was coming back up in the bathroom sink!!! In the middle of the superbowl, Home Depots are pretty much deserted...and here we were buying plungers, drain snakes, drain-o, monkey wrenches, and other plumbing tools. Luckily, all the other drains flowed OK in the house that evening.
The shower though has been running slower and slower, so just here recently, I made up a new pipe for it to tie into the washer hookup line that I installed a few years ago. The washing closet hookup, and the shower now share the same 2 inch pipe. I tested it the tub draining and the washer draining at the same time, and the shower drain sucks the water down so fast know you'd better get out the way, or it'd suck you down too!
My next task is to figure out why the water pressure is so low on the hot water side!!!