This is a thought that I try and in all of my clients with varying degrees of success. It's something that I think is a pretty small change, but one that will help determine success further down the road in someones strength training lifetime; both as a trainee and as a coach.
The idea is that of constants and variables within each exercise. The constant should be your form and the variable is any number of outside factors: intensity, load, time, tempo, etc. Just like with a science experiment, the more variables you have the more difficult it is to determine the results of that particular experiment (in our case, an exercise).
If you squat to a different, random depth every time you squat then how could you quantify if you're getting better at squatting or not? Yes "parallel" is a guideline, but watch any number of YouTube heroes and you'll see that the definition of parallel leaves some room for interpretation. Too, someone could tell you that they can do 70 pushups in a row, but each of their reps stops at some random point in mid-air.
Every exercise you do should have defined starting and stopping points (and these can be individualized based on the needs of each different person). These points should be full range of motion (ROM) for a healthy individual and should remain constant. For a person who's limited by mobility, flexibility or strength the starting and stopping points should remained fixed until the issues have been addressed and that client has been progressed on to the next variation.
Trainers/Coaches, be rigid about this. Don't ask your clients to always perform an exercise the same way, demand it of them. Repetition is the mother of retention. Every exercise should be completely reproducible unless you want it to be different somehow.
The other half of the "constant" is technique. If your client uses a different grip every time they bench press or do chin-ups, or a different starting hip position when they deadlift then you will have a different result each time. There is no single correct form for every person, just the general guidelines you should follow to get into the ballpark. Kelly Starrett calls this "informed dicking around"; once you know the right guidelines you can decide what works best for you. Once you've found the right technique and position for you, stick with it and groove it until it's time to change it for the sake of progression.
If we have ingrained form/technique to be our "constant" then we have room to start playing with the variable. This is when you, as the coach or trainer, is able to figure out what is working and what isn't. This is actually where the fun starts; you can start using all the methods you've read about and seen in SuperTraining, Westside Barbell and T-Nation.
Beware the desire to change all the variables at once. You wouldn't take the recipe for your grandma's apple pie and then change 8 ingredients and say "hmmm I wonder why this tastes like cherry pie". If you usually squat with a narrow stance, high bar position, normal speed and weightlifting shoes you'd have no idea what was happening if you started squatting with a wide position, chucks, tempo, pauses bands and on a bosu ball. Your squat would feel like shit because it would no longer be your squat.
Just like anything else you would do, work through progressions during different phases. Add tempo for one phase, then pauses, then both, then go back to normal to see what kind of results you got. If the client hasn't gotten stronger, figure out where you went wrong. Start out with a solid grasp of the basics and move forward from there.
Have a great day! Go lift some heavy shit!