I do not really think that there is a dispute between the two men in Act II. However, there is a dispute in Act I.
In Act I, Scene 2, there is a dispute between the two men. It is over a couple of things. First, Proctor does not like Putnam because the two of them have some disputes over some property. Proctor has taken wood of the property, but Putnam thinks it is his.
Second, Putnam is trying to control Parris. He has been behind calling Rev. Hale to come to Salem. Proctor thinks that Putnam should not be able to control things just because he is rich. This annoys Putnam because he feels that the town does not give him as much power as he deserves.