I am Japanese, but that doesn't mean I consider sitting in an onsen that has turned into a "niku jiru" a pleasant experience. There are some tactics in public bathing that we learn from our elders growing up as Japanese men.

1) Bathe at unsocial hours (and check the cleaning times of the bath - don't be the last one in!)
2) If it is at a ryokan and you have a chance to scout out the other guests (best done during dinner time), check what your competition is, numbers, age groups, what hair products do they use, etc. Try also to overhear any group decisions being made about when they plan to bathe. The popular slots are pre-dinner and post-dinner. Avoid these hours unless you want to practise Japanese.
3) Grease and debris float. If there is a water feature, you go there and stay there. The water flowing out will protect you from surface residues.
4)When it's really bad, it turns into niku jiru (when all the sweat and grease mixes with the water to make a stew/stock). You shouldn't really do this but I have taken samples with the bowl to take a closer look. Dip your fingers in and rub, how greasy is it?
5) Water should be flowing over the edge at all times. If it isn't, then what I do is check how wet the rest of the room is. (Actually you can do this in the changing room even before you go in). This will give you some indication of the bathing activity that has occurred recently. If the rest of the room is really wet and most of the shampoos are not neatly put away, then it is highly likely that there has been a 'dantai' (group) in before you and the likelihood of that compromising your experience is quite high.

Of course if you go to a ryokan with an onsen, then your checks should start early. If you see lots of coaches parked outside, then you know there are going to be loads of people. It is not unusual to nonchalantly ask at check in how busy they are - if it coincides with a wedding or a shanai-ryoko, then you have to work that much harder, be that much sneakier!

Japanese people are as filthy and greasy as any other, probably greasier, (helps with our famed "Nihon Gami" so well showcased in the Asiance - is this spelled correctly? - shampoo advert.)

I will only tolerate A+ conditions when I go to onsen. I wouldn't take my clothes off for anything less!