I've tested this on a multiplayer server running 15w43a. Zombies would not pickup anything.
I tested once again on latest 15w46a on my own pc using Windows 7. The zombies will not equip armor or weapons on the floor. They will not hold any item I throw at them. I tested different modes survival and creative. To see if the tracking AI would trigger it. Still did not work. I tested naturally spawned zombies vs ones I placed with a spawn egg. None of them would pick up any items. I did notice that zombies are spawning with random armor as usual. They just won't pick anything up. ,
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We did these tests on normal difficulty. I just tried changing to hard and easy. The difficulty does not fix the issue. We are spawning them with spawn eggs not a command. We also tried natural spawned zombies at night. Nothing I can do will make zombies pickup or equip any item I throw on the floor at them.
Make sure that mob griefing has not been disabled in that world, it will prevent pickup regardless of other settings.
Also not all mobs can pick up items, they have to have a flag which is set upon spawning. It may be that mobs from eggs don't get the chance for the flag to be applied now?
Will see if I can't reproduce.
I didn't test it, I just replied to the comments of the owner.
This issue is a duplicate, go and look at the original report
Well, do you know what the command should be, before I open a new (more specific) ticket or reply to an old one needlessly just in case I'm making a typo in the command?
The command you are using is incorrect. It should be as follows:
/summon Zombie ~ ~ ~ {CanPickUpLoot:1b}
Unable to reproduce. What difficulty is your game set to, and what command are you using to summon the zombie?