When DI Poole (Ben Miller) angrily pulls out the whiteboard, it has the names and photos of the case in episode 1.6, An Unhelpful Aid (2011) (the episode after this).
Early in the episode the characters mention Murder on the Orient Express (1974) which is a Poirot case. Later in the episode DI Richard Poole (Ben Miller) lays down a handkerchief before sitting on it. This is something Poirot does several times through the Poirot-book series. Also Poole is very detail-orientated something which Poirot is as well.
Sarah Smart who plays Suzie Park says "I Love a good murder" has starred on several murder mystery shows - Wallander (2008), Midsomer Murders (1997)....
Agatha Christie is mentioned in the first part of the episode two actresses have been in Poirot (1989) - Sophie Winkleman and Sarah Smart.
Actor Ben Miller has also starred on Marple (2004) in The Body in the Library (2004) as Basil Blake.