Frances McDormand's character Guinevere Pettigrew claims to be raised by a clergyman, when in real life, McDormand's adoptive father is Canadian minister Vernan McDormand.
At the big party, when Miss Pettigrew talks with Joe on the balcony, the boom mic is visible moving back and forth between characters in the reflection of the windows.
In the closing scenes Miss Pettigrew is seen leaving the nightclub through a dressing room. The "WAY OUT" sign was probably Lexan with indirect lighting. Lexan was not invented until well after WWII and not in widespread use until the 1980s. However, similar signs made from plate glass with a slight green tint were made in the 20s if not earlier, so the sign as shown is in reality true to the era.
On the balcony, Miss Pettigrew is talking to Edith. The two soldier extras behind Edith are in the shot. Edith switches places and the same two extras are in the shot on the other side of the balcony. As Edith switches back to the first side, the same two extras enter the balcony from the sides she is on. There's no way for them to have gotten from one side of the balcony to other in half a second.