Loki is responsible for the strife between the Avengers and S.H.I.E.L.D., but not in the way you think. Loki simply employs a 'divide-and-conquer' stratagem; he says things when he knows he is being watched/ listened to, with the intention driving a wedge between his captors.
Dr Banner notices Loki's crack about "a warm light for all mankind," which is directed at Stark, to make him suspicious of S.H.I.E.L.D.'s activities with the Tesseract. Loki likewise hints that he knows his prison was meant for the Hulk rather than himself, which helps unsettle Banner. He insults Black Widow openly, since he controls her unrequited love, Hawkeye. He calmly sits and watches Thor, Captain America and Stark fighting each other.
Loki played them like a flute, all the while having Hawkeye use Loki's staff to track the heli-carrier. But he doesn't use any of his powers to make the argument take place; he simply plants the seeds that cause the argument to break out.
EDIT: In light of the information from the director's commentary, it seems I was wrong. The staff did play a part. It would have been better film-making to highlight it more at the time, but whatever. Makes one wonder how Barton tracked the helicarrier, unless we are to believe the staff is responsible for both.