How does auto-pickup work?
Solution 1:
The auto pickup system specifically only picks up ammunition and money.
In co-operative mode you share ammunition so you never have to feel like you are stealing ammo from someone.
A possible explanation for the issues you're experiencing could relate to similar behaviour from the original Borderlands in that latency could allow you to pass an item without picking it up.
You're not the only one who has experienced this behaviour, several gamers are reporting the symptoms of ammunition and gold not being automatically picked up.
Solution 2:
Auto-pickup system only works on items (ammo and money) droped from monsters/destroyable objects (barrels,gas tanks,etc.).
All items from chests and containers can only be manually picked up.