Chet gets a marriage license more than a day before he learns that Jessica's last name is Vance instead of Jones, but when her father looks at it that same day, Jessica's last name is shown as Vance.
When Chet gets a bowl of ice from Jessica's new apartment, he leaves the kitchen with the ice below the rim of the bowl. But in the next shot of him outside the kitchen the ice is well above the rim of the bowl.