This 2009 adaption of Hamlet has a distinctively modern setting, with the use of CCTV cameras at the beginning confirming this. This was a choice by the director of the film, who perhaps wanted to make the story more relatable, interesting and relevant to modern audiences. The subject-matter, themes, and language of Shakespeare are universal and time-defying, meaning that the story can still make sense in the modern age. It is this universality that is captured when the story of Hamlet is set in a modern era.
Interestingly, the director also chose to cast Patrick Stewart in two roles in the film: King Hamlet's ghost, and Claudius. This decision has been criticized and misunderstood, however, it successfully illuminates a few key ideas. Firstly, it connects these two characters so visually suggest the connection between them. As we see Patrick Stewart playing Claudius, we are visually reminded of his dark connection to King Hamlet. This choice of actor also makes it clear that Claudius has metaphorically taken the place of King Hamlet.
Other than the choice to cast Patrick Stewart as two characters, there aren't any particularly revolutionary changes in this adaption. However, the film has been praised and celebrated for its faithfulness to the original play, whilst also adding a good amount of originality and intrigue.