Did a bit of searching around for this, haven't been able to find a clear answer: can an alchemist wield a shield with the tentacle gained through the tentacle discovery? Granted, he'd need to obtain proficiency first...
I did find a place where Sean Reynolds said that that sort of thing wasn't the intention of the discovery, but this seemed far enough from an official ruling that I wanted to seek clarification.
He said that the shield wasn't an intent for the vestigial arm, but that he'd let it happen.