They didn't just come up with Coppola directing, but he was their 8th choice after Sergio Leone, Peter Bogdanovich, Peter Yates, Richard Brooks, Arthur Penn, Costa-Gavras, and Otto Preminger were all offered the position and declined.
Albert S. Ruddy had already worked for Warner Brothers before he went to work for Rand and was then was a television writer at Universal Studios. He had already produced the film Wild Seed (1965) before he co-created Hogan's Heroes.
Mia Farrow appears to be at the table with Frank Sinatra, but this would have been 1970 and they were divorced in August 1968.
Ruddy states that McHale's Navy (1962) is a peace-time story. In reality, the show takes place during World War II.
Coppola's glasses have plano (no corrective) lenses. Coppola has myopia. This could have been faked with 3.2mm plano lenses that would appear as thicker corrective lenses.
During the pool scene with Mario Puzo, he is seen eating from a Corningware Spice of Life casserole dish. Spice of Life was not released until 1972 and the scene would have taken place in 1970.