Hate to mention it - but have you made a thorough search?
When my late husband first began having toilet problems, we had various scenarios. First of all - when he started to sit on the toilet, I was constantly finding the floor wet in front of the toilet. For ages, I was blaming our elderly cat!
Then I realised that when my husband sat down, the urine was actuallu leaking out between the toilet itself and the seat, and going down the outside of the toilet onto the floor! Then, as regards faeces, often what would happen is that he would feel the urge to go, but not get himself organised in time, and it would be too late. Trying to "hide the evidence" - he didn't know where to put it! One day I came in from the garden and met him just coming out the door, carrying it - in his bare hand! "I don't know where to put this!" he said - and went to hand it to me! So we managed to put it in the toilet, and scrubbed his hands with hot soapy water, and cleaned him up, and changed his clothes. Another time, I could get a horrible smell in the bedroom no matter how much I cleaned up - and discovered he had hidden "it" - by carefully squishing it down into the potted plants, like a top-dressing of compost!
I'm afraid it does sound like he needs more care or supervision. It's hard I know to bring these things up. It feels like a betrayal. But you have to think of the wider picture - with the scenario you describe, your dad is in danger of picking up an infection like ecoli, which can be very nasty and dangerous in the elderly.