After the dials are revealed, my buddy likes to saunter over to the opponents side of the table and take a good look at what the enemy is going to do.

Is this totally fine?

It's open information, so it's fine.

Usually dials are revealed one at a time in order of increasing pilot skill.

From the wording of your question it sounds like you've been playing mass reveal all at once, which shouldn't really be happening, and would be quite dodgey to look at what the other player does if that is how you play.

That said, if doing the dials one at a time there is nothing wrong with checking your opponent's move against his dial, so long as you do that politely and not every turn ("fly casual!")

Might come across a bit weird, like he is accusing them of cheating or something. Depends on his demeanor, I guess

No mass reveal! One at a time and there should be no need for him to do any sauntering. Why is he sauntering again?

It's not always easy to see dials from across a table and many players don't so much reveal as they do flip announce. A player is well within reason to ask for confirmation.

Yes, we have been operating mass reveals, but we'll stop that right away.

So, new procedure, lowest pilot skill reveals, moves and action. Then next skill up, reveals, moves and action.

Is that correct?

Yes, that is the way to do it.

Yapp that is correct Sir.

That actually prevents exactly what your initial question was!