For me, the one question is system. Van Dijk looks very good in a relatively compact Southampton team, who play a back 5. In a way similar to Joe Gomez did for England against Brazil, when you play with as much protection as VvD got, it can really mask his weaknesses. Liverpool play fan more expansively and can leave themselves open to 2v2s, etc.
Having said that, Southampton are pathetic without VvD and are conceding ridiculous amounts at the moment. Also, Klopp seems to have rectified the defensive lapses, with the goals we concede now largely being individual errors. Furthermore, there aren't many more defenders that I'd rather have than VvD in those sort of 2v2 situations.
In short, it comes down to whether he improves our backline. Sure as shit he does.
http://www.bbc.co.uk/sport/football/40730793 and here's a link to what the guy who scouted him for Celtic says.