What are some examples of puns in Act 3 of Macbeth?

A pun is a play on words through use of double meaning that is used for humorous effect.   In a tragedy it adds lightness to a dark scene and is known as “comic relief.”

In the beginning of Act 3, Macbeth is talking to Banquo about the banquet that night.

We should have else desired your good advice,
Which still hath been both grave and prosperous
In this day's council; but we'll take tomorrow. (3:1)

Macbeth’s use of the word “grave” here [grave: serious] is a particularly good pun because he is planning to kill Banquo and put him in his grave.

The best pun in Act 3 appears after the murderers return to Macbeth.

MURDERER:
My lord, his throat is cut; that I did for him.
MACBETH:Thou art the best o’ the cut-throats! Yet he's good
That did the like for Fleance. If thou didst it,
Thou art the nonparell.(20) (3:4)

Macbeth uses the fact that the murderer cut Banquo’s throat to make a pun about the murderer being cut-throat, which means ruthless.

In a dramatic and tragic play such as this, there needs to be some little jokes to cut the tension.  In fact, the play is quite humorous throughout because of puns.  Other instances of examples of comic relief puns are with the porter in Act II and the reaction to Banquo’s ghost later in Act III.  The puns allow the audience to fully experience the drama through cutting the tension every once in awhile.

In act 5 of Macbeth, what is an example of Shakespeare's use of a pun?

A pun is a play on words that exploits two possible meanings of one word or two words that mean different things but sound very similar, and this wordplay typically produces a comical effect (or shows the wit of the speaker). In one sense, then, some of Lady Macbeth's words while she sleepwalks can be seen as puns, though they might, perhaps be unintentional. However, they do produce a satisfying sort of irony in that she does not seem to be completely aware of the double meanings, at least not consciously. For example, during her sleepwalking episode, Lady Macbeth says, as though she is speaking to Macbeth, "No more o' that, my lord, no more o' that. You mar all with this starting" (5.1.45-47). On the one hand, she seems to mean that Macbeth ruins their happiness with his sudden starts and fits, the anxieties and fearfulness he seemed to feel way back when he committed the murder of Duncan. On the other hand, there seems to be another meaning of "starting," as in beginning, and she might unconsciously suggest that Macbeth actually ruined everything by killing Duncan in the first place. That is, after all, the thing that begins to drive a wedge between them, where they begin to feel so unhappy when they expected such happiness.

In Act V Scene i we see the Doctor and the Gentlewoman observing Lady Macbeth's sinister night time ritual of washing her hands after the murder of King Duncan. The Doctor comments-

Lady Macbeth is sleepwalking, and her eyes are literally open. However, this could be interpreted as a pun as she is also able to 'see' why she is in such at terrible psychological state. Similarly the Gentlewoman's response also has a double meaning-

Lady Macbeth is not alert to those around her and cannot see them as she is in her sonambulant state. She is also 'blind' to the perilous future her and her husband have unleashed on themselves having killed the king.