The problem with not feeding a dog what you wouldn't eat yourself is that you are not a dog, and you are not eating like an ancient human either (or even a modern human in almost any culture but our own).
You're not doing the dog (and probably yourself) any favors by rejecting, because of cultural preference, the "internal bits."

Humans did not evolve (or were not created) to eat, or even prefer only muscle meat (a distinctly modern american prejudice). The diet of ancient humans, modern humans in other cultures who know better, and even in this country just a few decades ago, included every bit of the animal that was edible. A wolf doesn't discard the blood or the liver, and neither did our pioneer grandparents (and neither do the English, Irish, Mongolians, Eskimo, Swedes and the Japanese, just to mention a fraction of the cultures that know better and do not throw away what Americans turn their noses up at).

These aren't just things that other people eat, because "they don't have a choice." The internal bits are often seen as the preferred, best bit. For some chinese, eyes are such a premium bit, they are either given to the oldest family member out of respect, or the youngest child as a special treat for luck and growth. In a wolf pack, much of the internal bits are the premium bits that only the highest ranking animals get to eat.

I guess I am just too "Americanized". ;) I tried blood sausages once and didn't do too well with them. I won't go near liver or tripe. I'm sure Bubba would love this stuff though.

Dogs do love liver and other organ meats. To the point they can eat way too much of it. Liver can have a bit of a laxative effect if eaten in excess (one year I found out the hard that this happens to humans too, by eating way eating too many rumaki (a bacon wrapped chicken liver and waterchestnut appetizer marinated in teriyaki sauce and then broiled).

When my brother and I were kids, we once slipped our small toy poodle quite a bit of liver off our plates (neither of our favorites as kids). We got in a lot of trouble for it, as it had the already mentioned side effect. Poor pup. (It didn't affect her love of liver though, we just had to be much more careful about portion control).

We bought our cat a cat food that was chicken livers, gizzards, and hearts. I'm not sure which one she didn't like or why, but they were all cut in the same size dice in three shades of gray/beige). When she was done, in the bottom of the bowl was a very well-licked bowl with a bunch of tiny cubes all of the same shade. So apparently one of them didn't meet her high standards.

Haha...that sounds like a cat! So cats like liver and all that? Does it have the same laxative effect on them? My cat doesn't eat solid foods, though. We give him a little bit of tuna or even solid food and he just licks it and leaves it for the dog to come by and scarf up...we don't give him much, just a pinch or two.