It was done because somebody did not know what they were doing. If you have a 2x8 and notch out 1 inch on the ends, it now becomes a 2x7 with some extra wood in the middle of those notches. Did it weaken your floor? Not necessarily. It depends on the size of the notched joist and its span.

If you're really concerned about the
weakening caused by the notches, you might
reinforce the ends using those sheet metal
Tecco joist hangers.

I gotta say that I can't figure out why someone would do that either but I disagree about the floor being weakened. Picture this...If the joists are bearing on cap plates at the ends and a beam in the middle (regardless of the 1 or 2 inch notch) what would be the difference between this scenario and one which we call an UP header or beam where the joists are hung (toenailed, tekkoed etc...) from the SIDE of the supporting structure. Like deck joists toenailed into a ledger board. It seems to me that the only thing you are reducing is the allowable SHEAR at the bearing point. BENDING which is what would really effect the structurable capabilities of the floor would not be reduced as you have not reduced the cross sectional dimension of the joist anywhere between the bearing points. A joist gets it's strength by placing material at some distance from it's neutral axis.. ie top of joist in compression bottom in tension (generally)(negative moments disregarded for conversational purposes)

The only concern I could see would be a
split developing from the inside corner
of the notch. Thus the idea to use hangers.

The full demension 2*10 has a 5 inch by 5 inch notch in it, I found it interesting that the builders would do this.

The hangers certainly wouldn't hurt. But They really won't do much for springy or sagging floors. 70 years isn't too shabby.

That's one hell of a notch. My guess is that builders are not the culprit. This sounds like a family project as was the custom way back when. As Kansaz said, 70 years isn't too shabby. If you really have no problems, then it should last another 70 years.