Continuity mistake: The clock in the hotel initially reads 9:21 and then abruptly changes to 9:20. (00:19:48)
Factual error: The stolen Sienese School painting is painted on canvas. Nobody painted on canvas in the 14th century, wood panels were solely used.
Answer: The man Red killed, Sam Scott, was Lizzie's adoptive father, not her biological one. However, at that time Lizzie (and thus the audience), was led to believe her real father abandoned her and her mother, so expect more secrets to be revealed how her real father actually died (or if he's even actually dead).
Bishop73