Which effects does the setting of the opening scene have on the play Macbeth?

The short opening scene establishes the dark, ominous mood that will dominate the rest of the play. The weather is gloomy, unpleasant, and foreboding. We are faced with thunder, lightning, rain, and three witches who are making plans to meet again. Emphasizing the eeriness of this strange, upside world, the scene ends with the witches chanting,

Fair is foul, and foul is fair
Hover through the fog and filthy air.

Meeting Macbeth is mentioned by them as well, which is mysterious. They note fog and filthy air—which, like thunder and lightning, is weather we associate with odd or even occult happenings. Finally, they tell us that things will not be as they seem, for what seems fair or good may be evil and what seems foul may be good. This supernatural and dramatic opening suggests we are heading to a dark and scary place.

The setting of the opening scene in which the three witches appear is actually quite scantily sketched out in the text and thus is open to directorial interpretation in plays and films that adapt the original. The only setting Shakespeare directly gives us is that there is "thunder and lightning" when the witches meet, and when they depart, they fly through "fog and filthy air." These clues establish an aura of eerie spookiness.
The setting serves as a premonition of the violence and evil to come. Though in the next scene we hear of Macbeth's victory and witness a celebration, the gray creepiness from the first scene lingers with us, and we know the good spirits won't last.
The setting also suggests that the witches interact with forces that are more powerful than humans are capable of using and have knowledge that surpasses human knowledge. They meet in thunder and lightning and fly away in foggy air. Thus, the setting tips us off to think about the role that fate/powers beyond Macbeth's control will influence the play's actions.