AJ and Tony are making sundaes and fooling around. When Tony was making a sundae he is using Pathmark brand whipped cream in a can. When AJ is in the kitchen and they fool around, the whipped cream turns into ReddiWhip.
When Big Pussy and Tony are playing pool the table is at a severe tilt. This is evident during Big Pussy's shot as both balls travel towards the left cushion and bounce along them as if the pool table is lifted. However, we find out in episode 11 that this is because they are using the inside of the pool table as a place to hide contraband.
In the flashback to Tony's youth where he sees his father beat up a man, young Tony is carrying a black-and-white composition book with a UPC barcode on the front. The flashback is set in the mid-1960s, but UPC barcodes were not introduced until 1974.
When in front of the amusement park, a sign is seen with a 718 area code. The scene is set in 1967 while the 718 area code would not come into use until 1984.
When Tony's father is driving his sister to the amusement park, there's a scene where he is about to park. There's a busy road with modern cars passing on.
When Livia meets Tony and Junior leaves, part of her observation about Junior is an overdub. When she says "...since becoming caporegime" her lip movement doesn't match the line.
In the overhead shot when Tony is telling Melfi that he was thinking of Jefferson Airplane, his lips clearly aren't moving.
Tony gets a flat tire driving near the Pulaski Skyway in Newark NJ, but he changes the tire in Long Island City, Queens, NYC adjacent to the Silvercup Studio where the series was filmed.
Likely intentional, but Johnny Boy calls Livia an 'albacore around his neck' instead of 'albatross'.