Evil scientists can be awesome (GLaDOS
, technically) or very, very stupid(Lex Luthor). However, sometimes the evil guy manages to be really stupid(like letting the hero unplug there own device. Why is it even plugged in?) Usually Played For Laughs.
These Scientists are capable of making reality warping devices, time traveling tech, and anything For Science. But they are incapable of getting things done to all the obvious ends since they leave their own undoing to the reach of the meddling kid and or the Hero. This however is more focused on the kids show but there are some details in other media such as films (Villains that don't take the Evil Overlord List as a reference).
Basically, you have a villain who is an "Evil Genius" - he's got the tech, the diplomas, and the minions to prove it - but despite all the faculties at his disposal, a five-year old could (and regularly does) defeat him at every turn, because he also happens to do mind-blowingly stupid things (like leaving the power cord to his death ray within easy unplugging reach) that prove his undoing every single time.
In other words, this trope refers to a disconnect between a villain's observable reputation and capabilities and the mistakes they make that allow them to be defeated - the guy is smart enough to build an engine that will catapult the moon into the sun. He knows his arch-nemesis is some stupid kid who keeps getting into his Evil Base. Why does he never think to keep the emergency self-destruct switch under a child-proof cap?
Doctor Doofinsmirtz from Phineas and Ferb. Not much to say here.
There's one Batman / Aliens comic where the mad scientist injects Batman's Rogues Gallery with xenomorph DNA to use as sentient superweapons (she also injects her own DNA, so they won't be able to attack her). However, when she does the same to Killer Croc, she doesn't use her DNA, so he attacks her as well.