First, I think there is a grey area between Turtle Dove's "never mention" an ex and always. Some stories involve both the event and the people there and are worth telling. I'm not sure why the grey area is so hard to explain.
The beach story is a perfect example. Another could be going somewhere on vacation and you comment that you know a great place for breakfast. A reasonable question or comment would be around why you're so familiar with the place. Answer, I used to go there all the time. Question, why X city. Oh I just liked it vs. an ex of mine had an apartment there. I don't see anything wrong with either answer, and wouldn't classify the latter as disrespectful to the person I'm currently dating.
Taking the issue of friends bringing up and ex. Think of playing cards as an example. Someone comments that they haven't seen a hand that great since you and your ex played one night. Kind of an innocent story, but the ex got mentioned. I don't see how that is disrespectful to the person you're currently dating either.
Another comment, "In my mind "not mentioning"="omitting". Isn't that what lie of omission means? That you simply "don't mention" something that the other person probably wants to know and deserves to know?" I think the key is that either they need to have asked or it needs to be completely obvious that they should be told. If you're talking about past relationships for whatever reason, omitting one serious enough to have resulted in an engagement is a lie of omission. Forgetting the person you went on one date with not so much.
On the other hand, failing to proactively bring up the fact that you were engaged in the past doesn't always rise to that standard. It is not obvious that someone needs to know or should be told and in fact, at least one person on this board would consider that disrespectful.