Aldis Hodge does actually play the violin, though not at a professional level as required for the piece in this job. While he didn't play the piece live for filming, he did learn it, and worked with his violin teacher to perfect the timing and fingering to make it accurate for the show.
In this job involving the theft of diamonds, Eliot impersonates a news reporter named Guy Hamilton. Guy Hamilton was the director of Diamonds Are Forever (1971) and three other James Bond films. However, according to the DVD commentary, the name was borrowed from the lead character, a journalist, played by Mel Gibson in The Year of Living Dangerously (1982).
The team often reuse certain aliases. In this case, Sophie poses as Christy Connelly, the same publicist persona she used in 'The Miracle Job.'
At 37:44 a close up of the check Nate is holding reveals that the name on the account is LEVERAGE ASSOCIATES with an address in Miami, Florida. The check is written for $500,000.
Timothy Hutton (Kragen) and Giancarlo Esposito (Senator Dillings) appeared together in Taps (1981) and Last Holiday (2006).