It is revealed that Arthur has cousins who live in Ohio.
"Arthur's Birthday" that takes place up through May 25th that is Arthur's and Muffy's birthdays together would be chronologically the last episode and/or book taking place during their 2nd grade year, as it has not been confirmed when their last day of school was in any book or episode.
Even though Francine gave Arthur a spin-the-bottle game for his birthday, it is implied that he either gave it away or discarded it since it's never seen again in later episodes and later books in the franchise; and due to the fact that it's a kissing game that isn't appropriate for kids since it implies sexual behavior.
This episode's calendar of the month of May with Arthur's birthday (May 25th) taking place on a Saturday is the same as with the May 1996 calendar, just like the fact this TV series premiered in 1996 as well as this episode. However, the book that it was adapted from, while it was published in 1989 and depicted May 25th being on a Saturday in the story, it wouldn't happen on a Saturday until two years later in 1991.