[You may want to skip this if you don't like frank discussions about the gross parts of human physiology.]
There are many ways to tell that after going on a low-carb diet, your body is in better shape. You start burning off excess fat, your blood sugar plummets, so does insulin, your triglycerides fall, your HDL level goes up, your LDL particles shift from the small and dense type that cause heart disease to the large and fluffy type that don't, you have more energy, you aren't ever hungry -- and so you rarely snack or nap -- and on and on.
But then there are lots of so-called cosmetic ways in which your body gets better. Your skin becomes more clear and supple, your hair gets thicker, your teeth look nicer even when not brushed, and you won't get rashes, discolorations, etc., that almost always come from allergies to non-animal foods. Low-carb people don't emphasize these as much because it seems superficial -- you should care more about your risk of heart disease than how bouncy the skin on your face looks.
However, natural selection designed the human mind to find signs of health visually pleasing because it was impossible to give other people a blood lipid profile test, measure their fasting insulin levels, and so on. Just because these features are on-the-surface does not mean that they aren't honest signals of underlying good health. So we should absolutely pay attention to our own surface when we try to judge how healthy we are.
Still, these changes may take awhile to become perceptible -- not years, but maybe weeks or months. How can you tell within days that a low-carb diet has put your body in better shape? Simple: judge the quality of what came in by what came out. Grazing animals that subsist on low-quality food like grass must eat a lot more than carnivores do. So they take in a larger volume of food, and most of that is useless junk that gets excreted. Such animals therefore defecate frequently and copiously. Carnivores do so rarely and in slighter quantities. That's why you can tell, just by walking around, whether there are deer in the area, but you couldn't tell if there were cats unless you saw them with your own eyes. (This is not due to burying behavior of cats; deer could try to bury theirs too, but there would still be too much to hide.)
One of my housemates is a vegetarian who occasionally eats cheese and even more rarely fish, though never eggs. Like the typical vegetarian, he lives on grains, legumes / pulses / nuts, corn, pasta, soy or rice milk, chips and cookies, etc., with only a small amount of colorful vegetables and fruits. That's why the name "vegetarian" is misleading; if you ate only colorful vegetables and fruits, you'd die from lack of protein, fat, and most vitamins and minerals. Human non-carnivores should really be called grainitarians. The only difference between him and a typical American, though, is that he follows this diet out of some higher principle (I've never asked), whereas the typical American feeds on mostly processed carbs and few animal sources without making a cause out of it.
To be blunt, when he's used the bathroom for number two, I can always tell -- visually. If a cat were toilet-trained, it would never leave streaks in the bottom of the bowl. Its high-quality diet just does not result in the streakable consistency of dung that you find among cows, elephants, and other low-quality eaters. And again, because he's vegetarian, he's in there at least twice a day, and probably a time or two more when we're not home at the same time. The cat would be in there only as frequently as it would use its litter box to defecate -- once a day at the most.
You've all been in a public restroom, so you know what it sounds like when others are there in the stalls. It never sounds like there's a well-formed one that goes plop, but instead like the microwave blew up their bowl of soup. I'm pretty sure that's mother nature's way of telling you to eat like a man instead of a 9 year-old boy. Only a sugar-sucking grain-muncher is going to make that sound in the restroom.
So unlike the other feedback your body gives you about how high-quality your diet is, this one is particularly quick at letting you know. How then do people ignore the inescapable marks that their food leaves? I think it's because there is little variation over time -- you would have to experiment with various diets in order to see how that affected what you left behind. Most Americans don't care that much about experimenting to improve their health -- I mean what the hell, someone else will bail us out if we get sick due to our own horrible eating habits. Some cultures might be more open about excretion, and so pay more attention to what it says about their food's quality, but that'll never happen here. *
In our fecal-phobic culture, the best way to avoid embarrassment about the sounds you make and the traces you leave for others to see is to cut out most carbs from your diet. You don't need them and they don't add flavor. There's nothing wrong with a daily fruit, vegetable, or other low-carb / high-fiber food like an avocado or almonds, just as a cat occasionally eats grass. But otherwise don't bother with a high carb load. Your bum and everyone else affected by it will thank you.
* We only pay attention if we suspect we've been infected by a pathogen -- to us that's more serious than following a lifelong diet of low quality because germs infecting our gut could kill us in short order via dehydration.