When Harry is being bullied at the start of the episode, his right shoe does not get knocked off when his trousers are pulled away, but suddenly appears next to him as the boys walk away. It makes no sense for him to then walk into town without it.
The wooded scenes in Holden, Kentucky supposedly take place in October, yet all the trees still have all their leaves. By October, in Kentucky, the deciduous trees are bare.
The bartender tells Jake that they only have Old Style beer, but serves him Falstaff.
The kid who got bullied said he had to get to school (drugstore scene). However, it was a Saturday, which we know because in the next scene (immediately after Jake asks the drugstore owner whether he could stay) Jake wants to rent a room for 3 nights, leaving on "the first", which is Nov. 1, as he is there to prevent a Halloween night murder. That would make it Saturday, Oct. 29, 1960 that he was in the drugstore and later renting the room.
One of the comic books seen low on the revolving rack in the diner in Holden in late October 1960 has a cover date of January 1961. It was common to have cover dates about couple of months ahead of when issues were stocked in stores, so a January issue in late October would be possible (though maybe unlikely in a small Kentucky town), but most of the other comics in the racks have cover dates in the spring and summer of 1960, so the newest one would more likely be displayed higher in the rack than shown here.
When Jake is in Holden KY with Frank and his buddies in the car, Frank tells one of his friends to "shut your pie hole". This phrase wasn't popular in the U.S. until the 1980's. Similarly, Frank's use of the phrase "help a brother out" is anachronistic.
In the bar, the bottles of beer they are served only appeared in the '90s.
Frank says that Jake is "probably an astronaut". Although the term astronaut was first used in the modern sense in 1930 and adopted by NASA in 1959, it did not enter everyday usage until the first manned American space flight in 1961.
The label on the Kaopectate bottle is nothing like the style used in 1960. It is closer to a style of label not introduced until 1971.
None of the residents of Holden, Kentucky have accents that sound even remotely like they are from Kentucky.