Bill mails his postcards after leaving the soda fountain, seemingly without putting any stamps on them, but on one shot while he's sitting at the lunch counter you can see stamps on the cards. However, in the next close-up, just before he leaves, the cards are unstamped. The likely reason is that all the closeup shots where he's writing on the blank cards were filmed together with the same camera setup, and the long shots were shot later after stamps were added. (Perhaps they filmed a scene of Bill buying and affixing stamps but decided not to use it.)
When Sam visits Daisy in early April 1917, a marching band on the street plays "Over There" -- which George M. Cohan didn't publish until several weeks later.