the heroine, and even theantagonist--all at the same time. Instead, all he sees is that he could play the parts well, as we see him state when commenting on playing the lion's part:

Let me play the lion too: I will roar, that I will do any man's heart good to hear me; I will roar, that I will make the duke say "Let him roar again, let him roar again." (I.ii.65-67)

His inability to see that there is a problem in his playing all three major parts and his excessive enthusiasm about his own performance abilities all help show Bottom is dumb as a donkey and arrogant. Also, while he does eventually give into Peter Quince as their leader, it certainly does take Bottom a while to back down from his request to play all three parts, showing how stubborn he is.

More importantly, his belief in his superior acting skills proves to be only an illusion, just as his belief that he is Bottom proves to be only an illusion when his head is transformed into the head of a donkey. His acting skills are proven to be merely an illusion both in act 3, scene 1 when he comes up with ridiculous ideas for the play and messes up his line delivery, and in the final scene when their play, which is supposed to be a tragedy, sadly makes their audience laugh. Hence, Puck's transformation of Bottom into a donkey also underscores the theme of reality vs. illusion, showing us that Bottom is not truly what he believes himself to be.

Puck is an inveterate trickster, a mischievous sprite who enjoys nothing better than playing silly pranks on others. High or low, mortal or immortal, anyone can find themselves on the receiving end of one of Puck's legendary pranks. It's this inordinate capacity for mischief that makes Puck what he is.

The latest butt of Puck's mischievous sense of humor is the hapless Nick Bottom, weaver and leading light of the amateur acting troupe, the "rude mechanicals." Bottom is a particularly appealing mark for Puck's latest merry jape. As well as having a funny name, his pompous personality means that he's just crying out to be made fun of.

The trouble with Bottom is that he takes himself much too seriously as an actor. Believing himself to be God's gift to the acting profession, he behaves in an overbearing manner toward his fellow mechanicals, making it clear to them that he's perfect for every part. In actual fact, however, Bottom is nowhere near as good as he thinks he is, and to any outside observer, he comes across as a bit of a ham.

One such outside observer is Puck, who finds Bottom such a ridiculously self-important figure that he cannot resist having a bit of fun with him. His transformation of Bottom's head into that of an ass is appropriate on two levels: firstly because Bottom's surname is synonymous with “ass,” or donkey, and secondly because Bottom's behavior shows him to be a fool, or an “ass.” That he displays the stubbornness of a mule is an added justification for Puck's mischievous prank.

In A Midsummer Night's Dream, Puck changes Bottom into the proverbial ass because that is precisely how Bottom is behaving. In other words, Bottom is behaving like an idiot. We especially see Bottom acting as an idiot when, in his excessive enthusiasm, he asks to have every lead role in the play. Quince has already asked him to play Pyramus, the lead male role, but when Flute hesitates to accept the female lead, Bottom says that he can play both parts. Likewise, when Snug hesitates to play the lion, Bottom says that he can play that part as well. Obviously, it is very ludicrous to think that Bottom could play all three parts at once. In addition, Bottom thinks a great deal of his skill as an actor, as we see in his lines, "If I do it, let the audience look to their eyes; I will move storms" (I.ii.22-23). However, we see just how ludicrous his overconfidence is in the rehearsal scene in which he keeps messing up his lines, such as the line, "Thisbe, the flowers of odious savors sweet--" (III.i.75). Obviously, "odious" is the wrong word as it refers to something that is "repugnant," or "disgusting" (Collins English Dictionary). Instead, Bottom was supposed to have referred to the flowers as having sweet "odors," meaning scents.

After Puck changes Bottom into a donkey, he is still an idiot, but he actually says something very intelligent; something that captures the heart of two of the play's themes. When Titania proclaims that she loves him, Bottom makes the very astute statement that there is no real reason for her to love him, and yet, reason and love don't really have anything to do with each other, as we see in his lines:

Methinks, mistress, you should have little reason for that. And yet, reason and love keep little company together now-a-days. (III.i.134-136)

This captures the heart of Shakespeare's themes that love is irrational and that the human mind is irrational as well.

Hence, we see that after Puck characterizes Bottom's foolishness by turning him into the proverbial ass, ironically, Bottom changes by actually making one very intelligent statement.

In Act III, Scene 1 of this play, Puck does transform Bottom's head into that of a donkey.  But I think you are wrong to say that none of the other actors notice that this change has happened.

First of all, the change itself happens offstage.  Bottom speaks a line and then says that he hears a voice.  So he exits and is, presumably out of view of the actors.  While he is offstage, Puck changes his head.

As soon as he reappears on stage, the other actors do notice the change.  They fear that he is a monster and they run away.

So they do notice that the change has happened.  They don't actually see the change happen, though, but that is because it takes place offstage.