What can we infer from Puck’s final lines in A Midsummer Night's Dream?

In Shakespeare's A Midsummer Night's Dream, Puck's final words (also the final words of the play) lead us to infer two main points: first, we can infer Puck is trying to accomplish the practical task of apologizing for any potential offenses within the play; second, we can assume that Puck is further advancing the theme of dreams, leading us to question exactly where the boundary between reality and illusion lies. 

Before going any further, it's worth looking at Puck's final speech in full:

If we shadows have offended,

Think but this, and all is mended,

That you have but slumb'red here

While these visions did appear

And this weak and idle theme,

No more yielding but a dream,

Gentles, do no reprehend. 

If you pardon, we will mend.

And, as I am an honest Puck,

If we have unearned luck

Now to scape the serpent's tongue,

We will make amends ere long;

Else the Puck a liar call.

So, good night unto you all.

Give me your hands, if we be friends,

And Robin shall restore amends. (5.1.412-27)

As you can see from the above quote, Puck is essentially asking for the audience to forgive him (and the rest of the cast) for any offenses they might have provoked. He's also asking for the audience's approval, as the line "Give me your hands" could be interpreted as a request for applause. All in all, A Midsummer Night's Dream is a comedy, and the jokes found in comedies can be offensive, and so we can view this speech as the playwright's clever way of covering his bases and assuaging any potential grievances.  

On a more subtle level, Puck is drawing us to question whether or not the action in the play was real. Puck invites us to consider that we "have slumb'red," and so he suggests that we too have fallen under some kind of spell and have simply imagined the hilarious comings and goings of the Athenians, the fairies, and the rude mechanicals. This interpretation adds another layer of complexity and ambiguity to the play, as Puck's final words lead us to question where we should draw the line between reality and dreams. There's no way of knowing whether or not we should trust Puck (he is, after all, a mischievous trickster), but we can infer that we should not assume anything in the realm of the play is entirely "real."