There are a few possibilities.
One, is that Tywin is a total and complete hypocrite, who scorns his son for whoring while bedding them himself. It shows that he is just like any other man in Westeros - he has desires just like any man, and he shits, just like every other person in Westeros.
The other, is that Varys planned the whole thing. He waited until Tywin went to use the latrine, then put Shae in his bed with the necklace of the hand around her neck, for Tyrion to find. Then he gets Jaime to let him out and lead him past the area in a way that Tyrion would know exactly where he is. This would make it look as if Tywin were a hypocrite and would just look worse after the deed was done. It would also give Tyrion some much needed vengeance because only Varys knows where Tyrion is going, which is obviously far away from here.
There's also the possibility that it was a combination of these of course, Varys planned the whole thing, minus setting Shae up. It could have been Tywin's own hypocrisy that was his undoing here, while Varys at least made the connections so that it could happen under Tyrion's own will.
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