The book this teleplay was based on contained quotations from Blue Oyster Cult songs at each chapter's start. Their hit song Don't Fear The Reaper plays over the end credits.
Shanker has a scar going from his mouth along his cheek. It's known as a Glasgow smile. In the book, Leda (Strike's mother) found Shanker having been attacked and bleeding when he was 16. She took him in and raised him alongside Strike.
When Robin gets back in the car, Cormoran is doing a newspaper crossword. He asks "Author of 'The Affluent Society'?". The answer is JK Galbraith, a clear reference to JK Rowling's pen name - Robert Galbraith.