Edit: The new flagging dialog is very good. As long as mods stick to Jeff's strategy (only declining when there is compelling evidence that the flagger wasn't trying to be helpful) this should be a non-issue.
The moderator will see the current version of the post only, not the version that was flagged. (I just tested this.)
If the edit occurred more than 5 minutes after the posting or previous edit, the moderator could review the history of the post. However, this requires time that many do not have, and also presence of mind that might not be reasonable to expect under all circumstances.
As for your feature request: I think that if the post is changed after you flag it, dismissing the flag as "declined" should really dismiss it as "disputed" (no effect on flag weight). That would be much easier than tracking the version of the post. We could call it "nullified" to distinguish from the normal "disputed" case.
I propose the same solution for when questions are closed and/or deleted after being flagged. Flags that have been declined should be auto-nullified when the post is closed or deleted for any reason. Our friendly neighborhood waffles has determined that approximately every 1 out of 6 declined flags, or ~17%, is for a post that gets closed. That's really high. This auto-nullify method would eliminate the trashing of flag weight for users who were probably doing the right thing to flag these to-be-closed questions.
Alternatively, something like the following could be displayed along with the flag, and the moderator given the option to dismiss as "disputed": "Note: Post was edited after being flagged." I prefer the method above ("auto-nullify on decline"), since it does not increase moderator workload and can never cause the user's flag weight to go down due to an edit occuring after the flag.
Another alternative: Auto-helpful if the post is edited by a 10k user (other than the flagger) or by a moderator. This has the downside of possibly marking some invalid flags helpful, so I still prefer "auto-nullify on decline".