Donald P. Bellisario established Sam Beckett's birth year 1953 by reversing digits of his own birth year 1935. However, in this episode, after Al tells Sam that it's 1965, Sam replies that he was ten in 1965.
When Sam arrives home at the beginning, and the director's credit appears, a chicken is seen standing straight on the front steps' banister post. In the next shot, however, the chicken is suddenly nestling down comfortably, its feathers covering the railing.
It states that Buddy Holly created the song "Peggy Sue" in 1956 but in actuality he records the song in 1957.
When Sam looks in the mirror, the person he leaped into is wearing glasses while Sam isn't.
In the opening scene, standing in ankle-deep mud, Sam holds a clean piglet, it should be muddy.
Sam looking into the mirror to see who he has jumped into will see what this character is wearing. If his counterpart wears glasses then the mirror image will show these even if Sam does not.
The calender in Doc's office displays the wrong month. August 1956 began on a Wednesday, not a Saturday as seen. As Doc would need to keep a close eye on the date to keep appointments it is very unlikely he would forget to change it. December was the only 31 day month to begin on Saturday in 1956. (September began on Saturday but only has 30 days. The calendar clearly shows a month with 31 days.)
Sam has to put right what once went wrong. Here he leaps when he inspires Buddy Holly to think of the song Peggy Sue, but Buddy Holly always did release Peggy Sue, so there was nothing to right in this case. The fact Sam and Al knew it was Buddy Holly almost singing Peggy Sue means he released the song in their world too. Although Buddy Holly released the song it was actually written by Jerry Allison and Norman Petty not Buddy Holly.