Really, if the show-within-a-show isn't the funniest part of your production, your mechanicals are doing something wrong.
Specific to a certain production (London, in 2006, by the Royal Shakespeare Company), but...
"'I go, I go; look how I go,/Swifter than arrow from the Tartar's bow!' Puck delivers this line with great enthusiasm... before plodding slowly off stage right.
"I am speechless and have nothing to say."
Oberon's "I am invisible, and will overhear their conference" is pretty funny considering he's been on stage, completely visible, for an entire scene.
One Shakespeare By the Sea production does one better by having Oberon, upon hearing the mortals approach, dramatically jump-dive behind a prop set, only to sit up and say: "I am invisible," then sit normally to overhear their conference.
The DC production also cast Lysander as an awkward loser of a guitarist. Cringe Comedy ensues.
"I say I love thee more than he can do!"
In the 2013 production at the Globe Theatre: Puck's pointing out that Oberon's instructions weren't clear enough ("Did not you tell me I should know the man by the Athenian garment be had on?"), and thus that the entire mess is his fault, was met by a subdued "Oh yeah."
The 2014 production at the Stratford Festival made the above scene even funnier, given that Lysander was being played by a woman. After Puck asks Oberon "Did you not tell me I should know the man...?", the actor playing Oberon gave Puck an aside glance, as if to say, 'I trusted you to be able to tell, Athenian garments or not, that that was not a man you found'.
Lysander's deadpan solution to the problem of Egeus' decision:
You have her father's love, Demetrius,
Let me have Hermia's. Do you marry him.
Bottom (James Cagney) in the 1935 film wanting to be Thisbe in the play.