Just so I'm not misleading anyone... It's not the mess of the oil that concerns me, although I'd rather not have that, but what the oil leak(s) may mean for the health of the car. If no damage is being done, as long as I keep the levels up, then I won't worry about it's table manners. (Yes, well said, Ken).
I do wonder if another grade or brand of oil may have less of a tendency to leak. for example, I've heard that good quality synthetic oil has a tendency to leak because it gets into places other oils do not.
I'm also very curious about the "mechanism" of this particular leak. Apparently the little hole I see on the bottom of the transmission is some sort of drain hole. And from what has been written above, apparently when oil leaks into some part of the bell housing, it can leak from that little hole. (I have no idea if this is so or not.) So, apparently the little hole is some sort of "safety valve" to draw off this oil, and "should" leak. All this because one of the inner seals is not holding properly. In all that I have read about Triumph TR3 transmissions, I have never found anything about this.