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This may or may not be satisfactory:

The flashback where Desmond talks to Charlie is very different from the other flashbacks (particularly the one in which Desmond meets Jack) in that Desmond actually remembers being on the island while living in the past and apparently remembers the events prior to experiencing them. I don’t think it is clear that the “deja vu” moments in this episode are supposed to be part of the past. More likely, Desmond is reliving these moments — and futily trying to change them — in some post-explosion dream state or semi-conciousness.

In the flashback, if Desmond does not claim to know Charlie (from the future), they would have just brushed by each other and never spoken.

I agree Chuck. The flashback where Charlie meets Desmond happens while Desmond is unconscious from the hatch implosion. During that flashback he experiences a lot of things and begins to remember being on the island. Had he not remembered being there he would not have actually met Charlie since the only reason they spoke was because Desmond recognized him from being on the island and approached him. In the other flashbacks we’ve seen, (for example when Desmond meets Jack) they are true flashbacks - meaning they are just the character remembering an event. Jack and Desmond met and spoke by chance so when they met later there was an existing memory. Desmond changed the past by speaking with Charlie so the event hadn’t actually happened until Desmond turned the key on the hatch. It would be interesting if after the hatch imploded and Desmond had changed the past if he then asked Charlie if he remembered them meeting on the street. That would explain if Desmond was actually changing the past or simply hallucinating during the flashback. It would also open Pandora’s box as we begin to play the ‘what if’ game with Desmond going back in time to alter events to benefit himself in the current time line. Sort of like in “Bill & Ted’s Excellent Adventure” when they needed something they’d say something like ‘Remind me to go back in time and get a gun and hide it behind this tree so when we get to this time there will be a gun here.” Then they look behind the tree and there’s the gun. OK now I’m giving myself a headache!!

If I casually (Desmond and Charlie’s interaction) ran into you a couple of years ago, neither of us would remember it. Desmond and Charlie’s interaction was simply not memorable. Desmond and Jack, though had a good conversation in which unusual (that’s the key) statement’s were made (training for a round the world trip, surgeon operating on a spine, etc.), while they were both doing the same thing, although unusual, the stadium run. People remember the unusual, and forget the normal.

I think Jack remembered Desmond, go back to the episode where he meets him I think he asks if he knows him or something.

I’m sorry, I misunderstood your post. Jack and Desmond do remember each other. When Desmond ran to his boat after he couldn’t fix the computer, Jack followed him. Desmond reconized Jack and asked him about Sarah. They both remembered each other. My point in my earlier post is they remember each other because of their initial interaction. Desmond and Charlie don’t remember each other because of their initial casual interaction. It simply wasn’t memorable.

I wrote a theory about this exact question. It is short and hopefully sweet. I basically state that Desmond would have never met Charlie if he had not turned the fail-safe key, and because of the butterfly effect, killed (on-island) Charlie. It is currently +13 and located here> http://www.lost-theories.com/theories/2007/oct/03/embrace-time-travel-if-only-10/