After my dog has done his business outside, he scratches his feet across the floor in the house and flicks mud and grass everywhere. Why does he do this?

Dogs will be dogs. It's a territorial thing. I have a female Shih Tzu and she does the same thing, after she has done her business. She is just marking her territory. It's not neurotic, just a natural instinct of an animal behavior. It does not seem practical that they are trying to cover their scent, since they pee on everthing they can find and even where other dogs have been and they don't try to stratch and cover that up.

Actually it is a territorial thing, and contrary to what others have posted, they are TRYING TO GET THEIR SCENT ON THEIR FEET! This behavior is also prominent in large wild cats such as lions. When lions patrol their territory borders they often spray landmarks to warn other groups of their boundaries. After they have sprayed, they do the foot motion in the same way that you see your dog doing. This is so that their scent can get on their feet and it can be tracked around their territory to confirm boundaries and ownership. My dog does this behavior too, sometimes at home, but usually at the dog park when there are other dogs around. He's saying, "Hey, I feel comfortable here and I belong here and all you other dogs should know it." It can also bee seen as a dominating display of behavior. He's letting all the other dogs know he is confident about his 'pack status'.

As a couple here suggested it is a territorial marking behavior!

While dogs PANT to cool down...the only place on a dog that DOES sweat is the pad area of their feet.

So, when they scrape their feet against the ground, grass or sometimes even a carpet...they are attempting to leave a bit of their scent behind..."this space is MINE!" or...a simple..."I was here!"

Either way, it's just part of their personal "calling card!"

Actually, it has nothing to do with covering his feces up, and everything to do with spreading its scent. It is a "territory marking" behavior, just like pissing on objects. Ordinarily he would do the foot-scraping, dirt-flicking thing around where he has done his business. He has been taught not to do his business inside, but he obviously considers the inside of the house "his" territory, and is still doing the marking behavior there.

I always thought they scratch furiously and 'kick back' their hind legs as a covering motion. I guess this is your pup's way of 'flushing' his business. One possibility is that perhaps your pup is a deep thinker and was preoccupied and forgot to scratch and kick until he got inside.

I think it has to do with an instinct to cover up his feces so as not to alert his enemies. Your dog may be just doing it a little late

This could also be like how cats bury their feces. Only alpha cats leave their feces uncovered. Since cats know that you're the alpha, they will bury it. Your dog may just be an odd dog, or as was previously stated, neurotic.

Your dog is like my dog...I believe it is a neurotic thing...The dog doesn't like their 'waste' getting on their feet...
Dogs or basically the canine species are very hygenic animals...meaning although they will basically eat other animals feces, they have a strong aversion to their own...and will make it a point not to defecate in anyplace where they will be sleeping...I think the foot scratching is basically to get any scent of their feces off of their feet.