Around the half of the movie, Holden takes Winnie to the baseball field because its his job and passion. He puts helmet on her head and give her a bat. He even pitched a ball to her from a mound. However, the baseball field was actually softball field (mound is flat - in baseball mound is elevated), her helmet and bat were also softball one, and Holden even pitched ball like in softball (underhand).
In Act I, Winnie and Holden get out of cafe and said each other "good night" - in the middle of day! In the next scene, Winnie is at her home and you can see through the windows it's still afternoon outside.
In Act I, Holden and Winnie are on date in cafe. Holden said that he is the agent of the most famous sportsman - Alex Halsey, baseball pitcher who actually doesn't exist. He either lied or production made up name for its sake.
Holden pronounced "leisure" as an American would but not like a Brit. Maybe he's been in the US long enough.