For this contract to be valid Mr. Wilson's offer needs to still be valid the next day and Dennis's smiling and walking away, and then coming back the next day and completing the act that Mr. Wilson had asked him to has to be considered an acceptance to Mr. Wilson's offer. So the legal issues present are with the agreement of a valid contract, specifically the termination of an offer and the acceptance of an offer. .
According to the book, Dennis can bind Mr. Wilson to his proposal or offer until the proposal is accepted or terminated. An offer can be terminated by: Revocation by offerer (Mr. Wilson), lapse of time, subsequent illegality, destruction of the subject matter, death or lack of capacity, rejection, a counteroffer and acceptance.
I do not believe that any of the stipulations to terminate an offer are present in this case. The only stipulations that could be questionable to terminate the offer are, lapse of time and subsequent illegality. I believe that one-day is not a long enough lapse of time. If it is Dennis's practice to do all the neighbors houses then there is a good possibility he was already busy for the day. As for subsequent illegality this is because one of the parties entering the contract is not of competent age. Dennis is only twelve years old but according to the book in a contract entered into by an adult and a minor, the minor is the one who has the capacity to terminate the contact. The adult must fulfill the obligation, unless the minor decides to avoid the contract. These facts should prove that the offer made by Mr. Wilson is still valid for Dennis to accept or agree with the terms. .
The next issue present is whether Dennis accepted Mr. Wilson's offer. When Mr. Wilson made his offer Dennis just smiled and walked away but he came back the next day and completed the act asked for by Mr. Wilson. In most situations silence or inaction on the part of the offeree (Dennis) does not constitute acceptance.