I agree with the above comments, the villains need to be connected in order to work.
Sandman and Venom didn't have any connection in Spiderman 3.
But, this whole Sinister Six concept, and with how Oscorp is behind almost all of the villains, makes the Amazing Spider-Man universe unique and coveres that need.
For example, Electro got his powers at Oscorp and Harry ran Oscorp. Harry freed Electro and got his own powers from Oscorp. So there was this connection.
The same will be able to be said with Doc Ock, Vulture, and most of the other Six. At the same time I think certain villains, like Kraven and Black Cat, can have the connection by being hired or lured into doing what they do best (i.e., hunting/tracking or thieving).