Anachronisms
Electric welds apparent on photographer's flash pan and on windmill vanes. Although electric arc welding had been invented by the early 1880s, it wasn't in common use until well into the 20th century.
Continuity
The shooting gallery at the fair has only 10 targets (2 rows of five). However, Anna shoots 12 of these 10 targets for a perfect score. Even during her shooting, there are short cuts to the gallery which still only has 10 targets but 12 shots are clearly heard and Anna wins the prize for perfect score.
Factual errors
Just as Doc Brown covers the DeLorean, we can see that there is no "Mr. Fusion" unit on the rear of the time machine.