Dynamic inconsistency, as defined in game theory, refers to a disagreement between your earlier self and your later self about what your later self should do.
More precisely, if your present self thinks "If things turn out like X, I should do Y", and then things turn out like X, and you don't do you Y, then this contradiction is called a dynamic inconsistency.
- Tuesday Self: If I buy whisky on sale tomorrow, and am extremely tempted to drink it before the weekend, I still should not do so.
- Wednesday Self: <Buys whisky on sale, feels tempted, and drinks it immediately.>
- Tuesday Self: I don't want to go swimming today.
- Wednesday Self: <Goes swimming.>
This is not a logical contradiction in preferences; Wednesday is a new day, and swimming could have different consequences on Wednesday (e.g., perhaps Monday made you too tired to swim on Tuesday, but by Wednesday you felt better).
- Tuesday self: I think smoking is worth the money.
- Wednesday self: <Finds out smoking causes lung cancer> Oh gosh, nevermind.
This is not a logical contradiction in preferences, but an update of your beliefs about what outcomes are possible/likely. On Tuesday you thought you could smoke without increasing your risk of cancer, and on Wednesday you found out you couldn't. Presumably on Tuesday you might still smoke if there was a way to eliminate the risk of cancer.