The reason why Toriko spent so much time trying out the exhibits at Life, the country of healing seemed to be so much different than his normal curiosity, was because it was different. Toriko is afraid that there won't be a cure to regrow his arm, and he is fooling himself into thinking about other stuff to take his mind off of it as most of us do. The exhibits aren't food, the only thing that actually gets Toriko excited, so it makes sense.
Some of the creatures in the Toriko-verse have abilities that seem a little too useful to be realistic. But the Rainbow Fruit hunt and Biotope 1 Arc establishes that the IGO does a lot of genetic engineering (The Troll Kongs being one example) and so it is more than likely that most useful animals are descended from some experiment.
Chapter 259's revelations mix this with a bit of Fridge Horror, explaining why humanity is confined to a small fraction of their own planet. "Human World" is actually the original Earth, the rest of the planet being a gigantic tumor created by a meteorite infused with Gourmet Cells. All of the more fantastic plants and animals in the series are actually invasive species.
After learning about Appetite Energy, the BB Corn arc makes more sense. At the time it seemed a little odd that the corn would enable Toriko to use more advanced techniques, as it wasn't incredibly tasty. But the Flying Forks and Knives are made of Appetite Energy that he releases subconsciously, and the BB Corn is special because it makes you hungrier when you eat it.
All of the Four Beast's victims survived being devoured. That might seem like an Ass Pull, but given the later reveal that the Four Beast was originally created by the Nitro to capture humans, not kill them, it makes sense. The Four Beast's unbalanced and insatiable appetite for humans isn't natural behavior at all; it's a design feature the Nitro added to make sure it would collect as many humans as possible.
It seems somewhat anti-climactic that after the time skip it's revealed Toriko was just allowed to take Komatsu back from the Bishokukai, but remember that Komatsu was able to win over Midora by satisfying him with a meal after he agreed to let any chefs go who could do exactly that.
I thought at first that Sunny learning about intuition and using it when trying to make a decision alongside Toriko's smell, Coco's sight, and Zebra's hearing is a bit odd, since it doesn't seem to fit with his theme of touch, like the rest of the Heavenly Kings who are related to a sense. But after thinking about it, it does fit with his theme, if a bit vaguely. Intuition, or instinct, is when you go by how your gut is FEELING, so it still fits in with the sense of touch, if barely. It's a little far fetched, yeah, but it still works kinda.
Alternatively, it can work with the idea of muscle memory and the ability to reflexively make actions.
As already stated above, each of the Four Heavenly Kings has a super-sense: smell for Toriko, sight for Coco, touch for Sunny (via his Prehensile Hair), and hearing for Zebra. Then there's taste... which represents all of them because they're all Gourmet Hunters.
How could GOD swallow the moon whole when Don Slime had destroyed it previously? Simple. Due to the earth in Toriko being much bigger then real life, it has stronger gravity, and therefore, attracted multiple moons.
Midora used to have an appetite like Toriko's. It's only after Frohze dies that Midora's appetite becomes unsatiable. He's trying to eat away the pain of losing Frohze, the closest person he had as a mother.
