Audio problem: When they scream at the cupcake shop, Gru sounds like he's behind the glass dome, while Lucy gives off a regular scream. But as we can see, Lucy is behind the dome, making a silly face, not Gru.
Plot hole: If the AVL was around during the events of the first film and aware of the moon heist then what was this organization doing while both Gru and Vector were doing their dastardly deeds?
Suggested correction: The AVL probably initiated an investigation regarding the moon's disappearance, but they wouldn't know where to look first. And it all happened very quickly, the moon was only returned to its original spot later on the same day, so they wouldn't need to continue with the case and could disregard it.
Other mistake: When Agnes screams after the evil minion tries to eat her unicorn, the noise shatters glass items and a sculpture on the mantelpiece as well as the evil minion's goggles. But Margo's glasses do not appear shattered at all.
Suggested correction: Glass shatters due to a loud sound because of a phenomenon called sonic resonance. If the glasses' natural vibration frequency doesn't match the frequency of the scream, they won't shatter.
Suggested correction: Her lenses could very well be made of plastic, which would not shatter like glass.
Continuity mistake: At the mall the double escalator in front of "Eagle Hair Club" appears and disappears several times between shots and scenes. (00:24:55 - 00:41:05)