Why did Gaston sign the check given to Juliette with the date 23rd and ask Mrs Al Smith to sign it with the date 24th (even though it was the same day ) ?

He did so because it was an opportunity for him to earn 100 thousand francs. He made her sign for 23rd as the property would then belong to him from that day onwards. As the property belongs to him on 24th he could easily sell it to Mrs. Al Smith for extra hundred thousand francs.