Arthur's 3rd grade teacher Mr. Ratburn was shown in the book, but removed in this Living Books adaptation since the story's setting is supposed to take place near the end of Arthur's 2nd grade school year as this kid's birthday as well as Muffy's are on May 25th - which they turn 8.
This is the first time in the franchise that Muffy is shown sans buck teeth (which she had in the book it was adapted from), but wouldn't be a permanent change until midway through the first season of the TV series that premiered two years later in 1996.
Arthur's school principal Mr. Haney makes a cameo appearance on Page 5 when Arthur and his mom go shopping for birthday supplies. Mr. Haney was not present in the book this was adapted from, but added in to fill the gap to represent the entire store scene. The illustration from the book was in close-up on one page showing only Arthur and his mom and an elderly lady whom is presumably either the storekeeper or another customer shopping while on the bottom of the page is the illustration of D.W. bringing in a big package for Arthur.
On the second page showing three students' drawings hung on the wall are the names Tina, Eliza, and Laurie. However, none of them by these names have made visible appearances in the books, computer games, or TV series. Eliza is named after Marc Brown's own daughter whose name frequently appears as an allusion on many props throughout the series.
Arthur and Muffy's birthday being on May 25th just like the book have that day being on a Saturday. In the book it was adapted from that was published in 1989, May 25th being on a Saturday wouldn't happen again until 1991 two years after that book was published and three years before this Living Books computer game adaptation was released.