(I'll start by saying all of this is MY OPINION. I'm not a bio-chemist, a vet, or a nutritionist. It's just MY OPINION. I don't want to argue about whatever I post.)
Wheat and corn tend to be ingredients that a lot of us shy away from, but as noted, not everyone does. The word "meat" makes me cringe. "Meat meal" or "Meat byproduct" is kind of scary. If they can't tell you what meat they're using from week to week, it's worth avoiding.
I prefer specific meat meals (chicken meal, salmon meal, turkey meal) over the meat (chicken, salmon, turkey) any time that there is grain listed as a top ingredient in the food. Otherwise, I'm getting a lot of water in the meat, and the grain is dry, so I may actually be getting more grain (pound for pound) than actual meat. With grain-free food, it doesn't
to me as much.
Corn syrup, high fructose corn syrup, dextrose, sucrose, molasses... learn all the names for sugar. If it's in your dog's kibble, you want to avoid it. Yeah, high quality sweet sorghum is supposed to be good for animals in small doses. You don't want your dogs eating it every meal. Sugar in your dog's diet means that they're covering up the fact that the food doesn't taste like it should. Avoid it. Salt (Sodium chloride) for the same reason, especially for seniors. If it's waaaaay down on the ingredients list, I don't stress about it too much, but if it's up there, that's a reason for me to look at other foods.
Also, a lot also depends on if your dog has allergies, and the only way to know this is to keep an eye on your dog. Most people tend to look at the big ingredients (the proteins especially), but the lesser ingredients are important as well. Some of the healthiest ingredients can cause adverse reactions. Alfalfa, flaxseed, barley, kelp. Often, people (and their vets) assume it's beef or chicken, but it seems to me (with my layperson opinion) that the other ingredients are culprits more often than the protein sources. But these ingredients are GREAT ingredients if your dog tolerates them, so you shouldn't automatically exclude them. Don't assume (as most vets do) that rice or potatoes are safe from allergies either.
As Jen says, dogs with issues need to eat what's best for them, regardless of the food's reputation. My puppy went from eating Innova (highly regarded) to California Natural (a more "basic" food) due to GI issues. What works for your dog is what's "best" for your dog, subject to what's reasonable, of course. I do think there's a basement level that we don't need to go below. There's no reason to buy grocery store dog food or certain brands. It isn't cheaper once you do the price analysis and it isn't "best" for anyone's dog.
Finally, read the label. Read not only the ingredients but also the Guaranteed Analysis. Is this what you intend to feed your dog? Does your overweight dog need 22% fat, just because that particular food (Instinct Turkey/Duck) has the right ingredients and lacks the "bad" ingredients? Perhaps you would be better off with another food that has 16% fat, like California Natural (16%) or Canidae (14.5%).
I'm not directing that last sentence at DHau, of course. I'm just saying: it's not all about ingredients alone. It's all a balancing game.