I haven't been able to get a follower to do anything except die.
I point to a door, "I can not do that."
I point to a spot on the floor, "I can not do that."
I point to a chest, "Oh, I wish I could do that."
Really? Why is that the only thing you can do is get in my way when I'm shouting at a Dragur or turning bandits into ice cicles or when I'm swinging a sharp object or shooting pointy things? Oh look, another dead follower.
That makes three. Well ok, two because the second one I sacrificed so I guess he really doesn't count.
The followers have the IQ of an apple.
It has to do with what they are already carrying.
When they search corpses, they pick up everything that was in the corpse's inventory. If that would put them over their encumbrance limit, then they cannot do it.
As for followers picking locked doors and chests, it's a very well done system. They have a random chance to open any locked door or chest at least up to Expert (I haven't seen any followers open a Master lock yet). When you ask them to do it, there is a random die roll to determine if they are able to open it or not, with greater chance to open lower level locks.
I've been playing a warrior character who doesn't pick any locks, so I've relied solely on followers for opening locked doors and chests. There is no need to add lockpicks to their inventory.