Let's just start with a simple fact: except as a part of a scheduled and organized physical fitness program, pushups (and other forms of exercise) are forbidden in the Cadet Program. There is no room for debate on this topic; it has been made crystal clear many, many times by NHQ/CP.
So, what can you do when Cadet Snuffy forgets to salute? Or when Cadet Bagadonuts doesn't button his pockets? Or when your flight at encampment has completely failed inspection?
Let's start with figuring out what pushups do accomplish. Why do soldiers have to knock out a few from time to time?
In Boot camp: Build fitness, get attention, wear you out.
Active duty: Get attention.
Outside of boot camp, pushups are merely a break in the action to give you time to reflect - and hopefully remember - what it was you did wrong and correct it. Active duty troops PT five days a week: what's an extra twenty pushups for being late for formation?
Now that we know that pushups following a mistake are merely an attention getter, let's do a quick examination of why you have the previous problems.
Why do Cadets and groups of Cadets make mistakes?
- They don't know how or forgot.
- They don't care.
Now, let's assume that Cadets Snuffy and Bagadonuts and your flight at encampment either forgot to do what they needed to do or just didn't know how. In that case, what they need is a little extra instruction. The extra instruction (which should be on the spot in the case of the Snuffy and Bagodonuts) should serve both to get their attention and to teach them correctly. So, pushups aren't necessary.
Let's say Snuffy and Bagadonuts didn't care, and let's say your flight at encampment got lazy. Pushups now? Nope: even if you could, there are better ways to get your point across.
If you're trying to make it painful for them to not do the right thing (Which is a leadership method of last resort - see below.), then pushups are one of the least painful things you can do. They knock out twenty and they're on their way snickering. Instead, we should take guidance from CP materials, which state that corrective actions should reflect the problem being corrected.
So, for Cadet Snuffy, who feels like he doesn't have to salute Cadet officers: about five minutes practice whipping salutes at the flag pole or the garbage can and rendering appropriate greeting ("Good evening, sir!") while under the watchful eye of a junior NCO ought to do it.
And for Bagadonuts, who's pockets are never buttoned? Well, can practice buttoning that pocket fifty times shouting, "ONE SIR! TWO SIR" in a loud and grotesque military manner the whole time.
And for your flight at encampment, who took too many shortcuts during cleanup and failed inspection? There's nothing like spending your free time on your hands and knees scrubbing to remind you that cleanliness is next to godliness and that flight sergeants don't like to be embarrassed in front of the First Sergeant.
All of those things are perfectly within regulations.
FInally, on the subject of punishment as a last resort: the whole idea of motivating your people by threatening them with punishment is just stupid: you don't motivate people with punishment, you motivate them with reward. Nobody ever did their best at something merely to avoid something unpleasant. When it's a perform-or-punish environment, people do the absolute minimum to get by.
You don't even train a dog that way!
If you want your people to excel you have to give them something to work toward: something that's valuable to them as individuals. It's up to you as a leader to find out what that thing is and get them headed in that direction.
Let me finish up by reminding you that pushups are a crutch for 'leaders' who are lazy and unimaginative. It doesn't take a rocket scientist to think up a better way - a within the regs way - to handle a situation where Cadets need to be reminded of their duties and responsibilities.