What happens when you get food poisoning in Minecraft (after eating rotten flesh dropped off zombies)?

Your hunger will go down quicker while you it is green, this isn't exactly bad, it just means you'll be eating more as it will go down quicker

Whenever the Hunger effect is applied to a player, it simply causes them to lose hunger at faster rates than normal. What this means is that running and losing health will drain hunger more rapidly, typically resulting in you being hungrier than when you ate the rotten flesh.

There's absolutely no disadvantage to eating rotten flesh to get yourself to full health / hunger, and is in fact quite strategic if you're low on food. Just make sure you stand perfectly still until the hunger effect wears off, otherwise you'll just be worse off than before.