You might find a range of different answers in response to this excellent question. However, for me, the definite turning point in the play comes in Act IV scene i, in the famous court scene, when Shylock looks as if he is just about to gain his much-desired vengeance, before he is stopped by Portia disguised as the famous lawyer. Note what she says:
Tarry a little; there is something else.
This bond doth give thee here no jot of blood;
The words expressly are "a pound of flesh."
Take then thy bond, take thou they pound of flesh;
But in the cutting it if thou dost shed
One drop of Christian blood, thy lands and goods
Are by the laws of Venice confiscate
Unto the state of Venice.
Note how, with this one speech, the situation of Shylock has been transformed from being a victor to being defeated and outcast. Up until this point, the action has steadily pointed towards this final confrontation, and the seemingly hopeless situation of Antonio and Shylock's ever more desperate desire to gain his revenge. This is the turning point, because it represents the moment when Shylock becomes defeated and Antonio now has power over him.