When Amy leaves prison after visiting Blake, they drive past an electric
taxi, which did not enter production until 2018.
Blake Fielder-Civil met for the first time Amy Winehouse in 2003. The movie shows that they met at a bar. On the wall, you can see a mural with multiple people and you can see Rihanna with short hair that was her look in 2009. Rihanna's first album came out in 2007.
In the bar where Amy meets Blake you can see "craft beer" on the outside windows. Craft beer wasn't widely available nor advertised in the early 2000s.
When Amy (Marisa Abela) is driving to the airport (around 1h05m), The Dublin Castle Bar signage is visible in the reflection of the cab's window (exterior shot of the cab showing Amy through the glass), but instead of being "mirrored", one can read it "forwards". This is clearly a deliberate choice by the filmmakers intended to make it easier for the audience to read, but technically inaccurate.
Blake Fielder-Civil was portrayed as a person speaking with a broad London Cockney accent when in fact he was born in Northamptonshire and speaks with a soft, middle-England accent.