On the morning news, the June 26th attack by the Son of Sam is mentioned. It is then mentioned that the Yankees won 5-4 the day before. However, the June 26th attack occurred at 3 AM in the morning, meaning the attack happened before the Yankees game on June 26th (which they did indeed win 5-4.) The game on the day before the June 26th attack would have been the June 25th game, which the Yankees won 5-1.
Reggie Jackson in 1977 did not sport a "soul-patch" beneath his lower lip. Facial hair for New York Yankees is prohibited below the lower lip. Back in the late '70s Thurman Munson, when in dispute with Yankee ownership, would from time to time begin to grow a beard, and then would be ordered to shave it. Over the years, other Yankees, such as Goose Gossage and Don Mattingly, have been reprimanded by Yankee brass for long hair or facial hair in violation of Yankee policy.
Many people have commented (in critic reviews and IMDB comment postings) that Billy Martin, born in California and having lived most of his life in New York, never spoke with a Southern accent as seen on the show. According to Jonathan Mahler's book, upon which the series is based, while Billy was a manager for the Texas Rangers, he loved Texas and it's people so much that he adopted the accent and the habit of wearing cowboy boots and hats for the rest of his life.
Several of the peripheral characters (policemen, the reporters prominently featured, etc.) are all wearing obvious wigs and mustaches to better blend in with the time period.
In the opening credits, a subway train is briefly seen. The cars have no graffiti, which was not the case for most NYC subway cars in 1977. Also, 2 of the cars are painted red with a logo depicting an older (R-10) subway car. In 1977, there were no red cars in the NYC system.
During the Opening Day scenes, the Milwaukee Brewers are shown in uniforms that they didn't wear until the 1978 season.
The song Boogie Oogie Oogie by A Taste Of Honey is heard being played at a Disco. The song was not recorded or released until 1978.
The Lite Beer commercial depicted was produced and first aired in 1978, by which time Billy Martin had been fired by Steinbrenner.