When Pops calls Adam, he's laying on the floor on his right side with the phone in his left hand. In the following shots, he has the phone in his right hand.
When Barry gets his Pennsylvania driver's license it shows his birthday as 9/03/1969 and the license issue date of 7/5/1984, making him 14 years 10 months old. In Pennsylvania, permanent (laminated) licenses are not issued to people under 16.
When Barry pulls in to the "kegger in the woods" he parks behind an '87-93 body style Mustang, which has faded paint and rust on it. Seeing as the oldest model of this body style was only 2 years old even at the end of the decade, this would be highly unlikely.
Murray is trying to watch the Phillies in the World Series, which would set the episode in 1980 or 1983. Barry just got his license which had an issue date of 7/5/1984 and the registration sticker on the family station wagon was 1986-neither of which align with a Phillies World Series appearance.