At one point the British spy Hagarty says that during the shootout before the interval (aka intermission), it was fortuitous that the 1812 Overture was playing to cover the sounds of gunplay. When played in a concert, the 1812 Overture is only ever played as the last piece - never before the intermission.
Haggarty, the spy, was walking around in a white shirt with two blood marks on the arm where he was supposedly shot. There is no damage to the shirt though. Surely there would be a couple of bullet holes in the shirt sleeve.
Boom mic visible when violinist rehearsing on stage.
During the car chase through the streets of Washington, DC, the party is driving from the Kennedy Center to the British Embassy. The first scenes are of the cars leaving the Kennedy Center. They drive by many notable Washington DC sites, only to once again pass by the Kennedy Center in the last scene before arriving at the British Embassy.
Guest star Jenny Agutter's character, Margo Claymore, talks about being from Rhodesia. While Margo might've been from Rhodesia initially, at the time this episode aired (Oct. 1986), Rhodesia no longer existed, having been split between Zimbabwe and Zambia in 1980.
Margo Claymore, dressed in a white evening gown, asks everyone in the room if they'd like something to eat. Her husband informs her that the servants were sent home. She excuses herself to go to the kitchen to prepare food on her own. After the murder takes place in the garden, Margo appears outside, still dressed in the white gown, to ask what happened. Why would she still be wearing a white gown to work in the kitchen? Hours pass and no food is ever made nor served to anyone.