Yanks cannot be pigeonholed so easily. As busterbill says,
I'd have to go with context, tone of voice and body language. I have heard each phrase uttered with an entirely different intent!
- And it's the same with me. Now for the nitpicking:
I don't think I've ever heard "With greatest respect - " used as a preamble at all in conversation. That is stiff and unnatural to my American ears, and the choice of words makes me suspect Ben's source was no Yank. Now, the superficially similar opening formula "With all due respect"
is a standard US usage, but it's very specific in application. I would expect it to be British English as well, but in case it's not, here goes: It acknowledges authority, or it is used to confer a degree of respect - possibly superficial or even false -
but in every case it signals a contrary opinion, so that's to be understood from the moment you hear it. It is code only in the sense of convention, not in possible ulterior meanings (if they exist, it is only in the speaker's inner monologue, which is irrelevant to the plain fact of demurral within a social context). As a stock introduction, the wording is not open to variation, and it's not normally used for any other purpose. It's a diplomatic way of saying, "Yeah, but..." to someone in power; in fact, a simple "With all due respect!" might stand very well as a shorthand protest to your superiors, all on its own. Or you might use it to pay kind lip service to someone's cherished stance on a matter before you proceed to pee on his roses. Barring that, I'm least likely to say it to a social equal. In any case, when someone opens with, "With all due respect", in the flesh it's not that hard to gauge their sincerity. Print of course would be tougher. Now, in the unlikely event that I did use "with greatest respect" in any fashion, it would most likely be in a public address praising someone in the third person, and the audience's agreement is already presumed. Or I might use it when signing off in a letter, especially if there's real gratitude or the like involved; no hidden "you're a putz" message would be embedded. The recipient's level of paranoia is another matter, though, and what can be done about that? But as an American I definitely would hesitate to use it face-to-face. It's too formal, too wooden, too nonstandard and too obsequious for my self respect, whether I meant it or not. Even worse, it could backfire because it's highly likely to embarrass the recipient. It would backfire on me; it has way too much smarm and cholesterol for comfort. It's a style thing. OTOH, I might use it ironically from atop my throne in my high tower when addressing some detested rival that I mean to squash like a bug - but guests are so few these days. The question, then, is less about what we think it means, than why and how we would use it.
In short, to believe that Yanks might universally take "with greatest respect" at face value is to believe that we could be one-dimensional marionettes. Not that that is what you believe, Ben, but all the same I'm here to assure you that we are not. The fact that you're never quite sure about us should be proof enough that while we might have a different angle, we are just as devious as you lot.
I always take "I'll bear it in mind" as a polite brushoff, just to be on the safe side; I've used it that way myself. But not every time! And that is precisely why you have to be on your toes around us.
benhall.1 wrote: How about, "I have just a few minor comments ...," or, "Very interesting," or, "Oh, by the way ..."?
I see nothing significant to read into the first and third. Why should I? I have little to no interest in what subtler subtexts might be behind them; just say your piece and get on with it, and then go seek counseling for your demons if you must. When I say them it is simply because afterthoughts have arisen, nothing more. Now, inside I may have accompanying judgments about my audience, but I just as well may not, and for that reason such judgments are irrelevant; they are my problem, and have no bearing on the simple fact of the communication at hand. One might use them for a bit of flair when delivering zingers, but it's not the main reason I use them. That's just an added benefit.
As to the second, it depends.
Well, it does to a Brit. 
