The ages of Judy Garland's daughters Liza and Lorna at time of 1954 A Star is Born release would have been roughly 8 and 2 years old respectively. In this film Liza is played by actress who is at least teenage while Lorna is played by a grade-school age actress.
Judy watches color TV broadcast of A Star is Born on a vintage black and white television set.
Fake issue of Variety with news stories on back cover. Real issues of that publication always have ads on back cover.
Judy sings the wrong "Eli Eli" to Louis Mayer. We hear her sing an Israeli song that begins "Eli Eli" but had not yet been written at the time. (It's more properly known as "Walking to Caesaria.") An entirely different "Eli Eli," one of the most popular Jewish songs in the early days of the phonograph, is what we should have heard.
When Vincente Minnelli empties the Q-tip jar while looking for pills in Judy's dressing room, a bar code sticker is clearly visible on the bottom of the jar.
When Roger Edens and Vincente Minnelli are talking to Judy about being suspended, you can clearly her her daughter, Liza practicing her lines off camera saying "Mama watch me, watch this"