@RomanceDawn:
There probably isn't a single level of crazy she actually is. I'd say its kind of like the Hulk. We know even during his nuttiest Hulk outs he can still talk, listen and formulate ideas, plans and strategies, they are just kind of limited to that of a 4 year old.
I like your Hulk comparison, but Big Mom is having some pretty complex thoughts right now ("Let me first call Zeus and Prometheus, then command Napoleon into Blade Form, then time this leap in order to land on Zeus wants he gets here, then use that to jump over to the ship"). Like, she's straight up REASONING with Jinbei ("If you want me to get off the ship, then give me the cake", or "My son told me the cake was here, if it's not I'll have to kill him, so when you say the cake isn't here, you're insinuating that he's a liar, and that angers me!") when compared to someone like Hulk ("I'm gonna wreck it!").
@RomanceDawn:
When her cravings first act up there could be a huge wash of sensations that overtake her, now though she has been starving to the point that in a single day it has physically altered her outer appearance. Who knows what that could be doing to her mind. Her brain could very well be adjusting just enough to process things around her better. Perospero certainly didn't think she'd remember his little lie. Don't forget a huge part of this particular hunger mode is unprecedented for all the Big Mom Pirates and most likely Big Mom herself. There is no history to compare her current state to.
Then she should be able to continue on this path until she comes back to her full senses, at least enough to know to eat something else just for the nutritional value while she's chasing cake. I mean, she herself KNOWS she's starving. I don't understand how Perospero is in any danger right now, as it seems that Big Mom is in such a useable state of mind that she could simply decide NOT to kill him. Anyway, I know it's for the sake of plot-armoring the Strawhats, but it was an odd way to do it, is all.
@.access:
I think the thing with Linlin is she is a hungry person taken to the extreme. Everyone knows someone who becames easily irritated when they are hungry, start lashing out at everyone and everything and can't be really reasoned with. With BM I think it's just that, it's not that she loses her ability to rationalize, it's just that she is too damn hungry and pissed to actually think straight and give a fuck about anyone or anything except eating what she wants. Remember she is not the most sane and emotionally stable person, she has very little emotional intelligence to handle the frustration that comes from not getting what she wants.
This would also mean that at some points she would be less able to listen to others while at other moments she would be willing to think straight, in a fluctuating state of mind, like RomanceDawn suggested.
I understand that the "Hangry" condition might exist in One Piece. But if she was as you described, then the behavior we've seen from her should've been REVERSED, with her starting out in this current persistent-yet-aware state, THEN regressing to screaming "Weeeeding Caaaake" and pulling peoples' souls out their faces like she was in the beginning.
@BattleFranky69:
…was the first time she was ever so conflicted about which thing to get the most pissed about it actually put her on a delay...
Hoo, boy. I had forgotten all about that little plot point. Definitely need to go write up a best/worst of the year post…