The problem with forgetting what the academics say and going with personal observation is that personal observation is so easily biased. It's very simple to diagnose "dominant" behavior in your dog when you are looking for it, even when there are other perfectly logical explanations. It blinds you to other possibilities because it is so amorphous and poorly defined.
For example, many people say that a dog who jumps up on them in greeting is 'dominant.' Problem is, this is a classically submissive gesture. Juvenile canids will run up and lick the mouths of family members returning from the hunt to stimulate regurgitation. As they mature, this licking behavior becomes a greeting. It's called an 'affiliation display.' Dogs also attempt to perform an approximation of this (it's buried in their genetic heritage) with us, it's just that our faces are so much higher from the ground . Hence, they jump.
It is not totally inaccurate to say that dogs display dominance and submission, its just that people have misappropriated it. These are part of dog communication, but they are not personality traits. You cannot say a dog is dominant (in ethological terms) because that is a misuse of the term. Dominance simply means " priority access to resources."
We want to say that a dog who shows dominant signals is a dominant dog, but all dogs regardless of social confidence use both dominant and submissive signals to communicate. You never have a dog that shows dominant signals all the time unless they are totally unsocialized or have serious behavior problems. The same goes for submission. It can happen, but this is the exception, not the rule and should not be mistaken for normal canine interaction.
I too watch my dogs.
One of them displays much more dominant signals than the others in social interaction, and they usually defer to her at meal times and with specific toys. Yet, she lets one of our males mount her in play. She takes the worst sleeping spot available when we crash for the night. She will let our smallest wrestle toys and bones away from her, when she could easily overpower him. If there were some underlying pack hierarchy, logic would dictate that, as the dominant dog, she would always have access to "the best of the best" in the house. That is simply not the case.
The biggest problem with dominance/pack theory is that it utilizes comparative zoology. It attempts to use (outdated) models of wolf behavior to explain the behavior of modern dogs. It's a bit like using Victorian knowledge of chimpanzees to explain modern human social behavior.
A note on wolves: Dominance theory was born out of a mid 1900's study on wolf behavior. We know now that wolves are family groups, the "alphas'" are simply the breeding male and female, and the rest of the pack their offspring. There are no dominance struggles for leadership because no son or daughter will overthrow one parent to mate with another, it's ludicrous.
Where we got the idea that this happens is from said study, where we took a group of unrelated individuals, put them in close quarters under stress, and watched as they fought after we totally disrupted their normal social system.
Until more studies (by some of the same scientists) were done with wild wolves in the 1970's, we erroneously applied this theory of a rigid social hierarchy maintained by aggression not only to wolves, but dogs and all other canids as well.
Regardless, it's a mistake to equate wolf pack behavior to dogs because their social systems are very different. Wolf packs exist solely based on the availability of large game (interestingly, in areas where large herbivores are unavailable, wolves actually don't pack). Wolves are monogamous hunters, their packs exist to co-ordinate large hunts and rear successive generations of offspring.
Dogs, on the other hand, are non-monogamous, and primarily scavengers. They form what are called "loose associational groups" whose social dynamics are far more fluid than wolf packs. Because the relationships are not famillial, members come and go as they please. There is often no one "dominant" dog, rather, many dogs may take on a more "dominant" role on different occasions, or even between tasks. They don't need to co-operate for hunting. Males and females do not stay together to raise pups. Some feral dogs live completely alone. So why do we insist that dogs "pack" at all when all the criteria of other packing canids are not met?
Whether or not you want to subscribe to the theory, there are a few reasons why I really try to discourage it in regards to training.
1. Dominance does not = aggression
(this is one of the dangers of calling dominance a personality trait). Aggression is a distancing signal. The less confident a dog is, the more aggressive it is likely to be.
When a diagnosis of dominance is given to a dog, the only logical solution to that is to reduce that dog's dominance/increase your own. Right away, this sets you up in an antagonistic relationship with your dog. Every misbehavior is personally directed at you and is your failure to "be a leader" to your dog. The prescription for dominance is usually forced submission, and usually corrective. This will almost certainly exacerbate your dog's behavioral problem because aggression is almost always fear-based. Introducing corrections or intimidation to a fearful animal will increase their fear, not alleviate it.
2. It's not a real diagnosis
. Even among people who believe in dominance, there is no clear definition of dominant behavior and what it constitutes. There is only personal observation.
Recently, we worked with someone who had a border collie who was becoming reactive to cyclists. She was worried he was showing dominance, based on the diagnosis of her dog walker. We calmly explained that this is simply a border collie displaying herding instincts. Herding instincts are hardwired. They are a fixed action pattern. No amount of 'dominance reduction' will change his drive to herd, it can only be re-directed. If she had tried to address his emotional arousal to bicycles with corrections, she may very well have turned excitement into real aggression (because bicycles will become a predictor of punishment).
3. It's misleading
It creates a level of mysticism around both dog behavior and the trainer. Whenever something works well and the trainer cites their own "dominance," regardless of what mechanisms are really in play, they set the dog and the owners up to fail. There are a hundred reasons why a trainer can get a dog to perform where the owner's can't (the situation, their body language, a dog's level of shutdown, etc.). When these people try to reproduce the same training techniques (if they haven't been told the real mechanisms by which they work) they often have mixed or even regressive results and they have no recourse other than stepping up their level of correction. It doesn't give people the tools they need to deconstruct a situation, identify the triggers behind it, and come at it from multiple angles or with different techniques.
4. It's counter-productive
There is no evidence that some of the more harmless dominance reduction exercises produce any change in behavior (other than simply altering a dog's expectation in a given scenario) and a wealth of evidence that some of the more intensive ones create behavioral problems.
In case you've read this far, here are a few of my favorite books and articles on the subject