The first thing we learn about Macbeth is how "brave" he is (1.2.18). His actions are described by the Captain, who calls him "Valor's minion" due to his courage in battle (1.2.21). This, surely, is a strength no matter how we look at it.
After he hears the Weird Sisters' predictions that he will become Thane of Cawdor and then king, and the first part of the prediction comes true, we see that Macbeth is ambitious because he would be happy to possess the crown. He says to himself, "Glamis and Thane of Cawdor! / The greatest is behind" (1.3.125-126). In other words, the best part of the prophecy is yet to come. Many would consider ambition to be a strength, but because it leads him to behave in unscrupulous ways, we might think of it as a weakness. He will become more and more ruthless in his quest to gain this title as the act progresses.
At first, Macbeth does not incline toward violence in order to satisfy his ambition. He says,
If chance will have me king, why, chance may
Without my stir. (1.3.157-159)
He hopes that since the title of Cawdor fell into his lap that the title of king will too. However, once he learns that Duncan has named his son, Malcolm, as his heir, Macbeth realizes that if he wants to become king quickly, he will have to resort to violence. He says,
Stars, hide your fires;
Let not light see my black and deep desires.
The eye wink at the hand, yet let that be
Which the eye fears, when it is done, to see. (1.4.57-60)
He asks the stars to put out their light so that no one can see the evil things he's wishing. He won't let his eye look at what his hand does, and yet he's still going to do the thing that his eye would be afraid to watch. He has resolved upon violence. Such a speedy transition shows that Macbeth is relatively easy to corrupt. For a moment, he hopes he will have to do nothing untoward in order to ascend to the throne, but the moment he encounters the very first obstacle, he resolves to murder. Thus, we learn that he is disloyal as well. We don't often think of these qualities as strengths.
In the next scene, Lady Macbeth's reaction to his letter allows us to get a clearer picture of what Macbeth was like before the play began. She fears that his nature is "too full o' th' milk of human kindness / To catch the nearest way" to the throne (1.5.17-18). She believes that he is too good to consider violence as a means to that end. He must have been a fairly compassionate and gentle man prior to the war and the prophecy. She obviously considers this a weakness and would applaud, as a strength, Macbeth's growing ruthlessness and disloyalty. For Macbeth, himself, his growing brutality leads to his undoing, so we might consider it a weakness.
We see, in Scene 7, that Macbeth does have a conscience, at least for a time. He hallucinates as a result of his anxiety prior to committing the murder, and he does attempt to back out of the plan. However, when Lady Macbeth insults his manhood, wounding his pride, he once again resolves on violence. Thus, we have further proof of how easily corruptible he is as well as evidence of his excessive pride, both traits we would consider to be obvious weaknesses.