This is a new system to the game, so I understand it having some kinks to work out. But there are a few in relation to how they behave that I think really should be implemented.
Have companions be smart enough to move out of AoE damage circles.
You put them in the game so we could know where the damage is (the circles, I mean), which means there's some system already in place that the companions should also be able to react to. Just associate the two.
Don't have companions waste stamina dodging nothing.
Sometimes a companion will dodge roll when not in any actual danger. Although this is fun to watch, if they have actual stamina limits this is extremely wasteful and puts them in danger of running out when they actually need it. Only have them roll when escaping a dangerous location or actually dodging a melee attack (since an already fired ranged attack is essentially homing in this game; a roll dodge wouldn't help).
Make companions stand *behind* you unless they *have* to be in front of you.
Believe it or not, this is the big one for me. I can't say how many times I've gone to collect a resource, talk to an NPC or do some other thing, sometimes in the midst of impending combat, only to find myself talking to Bastion or Mirri because they ran up to EXACTLY WHERE I WAS LOOKING and stood there. This is hands down THE most annoying thing companions do in game.
Just now, after completing a mission, just as I was about to talk to the NPC who completes it, Bastion walked in front of me, stood on top of said NPC, and started talking about how much he liked fires. I wanted to kick him into it.
Remove companions urge to complain (or worse, lose affinity over) about super trivial things.
I am in a dungeon, fighting three enemies. I use Elemental Blockade. Bastion suddenly yells, "Stop that! It's cruel and wasteful!" ...why? Because I hit a rat on the floor with the spell while fighting enemies. This is stupid. Why would catching butterflies, a required alchemy resource, cause you to lose affinity with someone? Can we not explain why we're doing it to them? And one is a mage, while the other is versed in Daedric knowledge; do neither of them understand alchemy? Why is the unintended death of a random rat in some mold encrusted dungeon during a battle for my life enough to catch Bastion's attention at all?
I understand things like actual murder or thievery. But killing vermin or bugs (which by last RL ratios is 200 MILLION to one) *should not* cause affinity to decrease.
Companions should not continue to instigate combat if you stop.
I know that, in basic monster behavior, a monster that agros on you will chase you for a ridiculous distance just to get one hit in on you, then lose interest. This should NOT be the case with companions, who could conceivably get killed while trying to fight something that you're not aware of on their own.
Example: Someone was running towards me with a Bog Dog chasing them in Blackwood. It was getting close, so I fired off a 'warning shot' (a ranged attack that seems to snap enemies way outside their range out of whatever berserk haze they get into and makes them run back to their position) at it. Bastion suddenly said something, then ran off after said Dog, who had dropped agro and was leaving. Behaving very similarly to the enemies on the map, he proceeded to *run so far off I couldn't see him anymore* before coming back. This shouldn't happen.
Since I am not at all confident that Bastion or Mirri alone can handle monsters (at least not at their early ranks and gear setups), I don't think they should go that far on their own to try to engage an enemy, especially since they don't seem to have any threat determination... Bastion would have run off after one of those huge dinosaur looking Argonians just as soon as he would have that Bog Dog without a second thought. Worse, said Argonian would have eaten him out of my line of sight, then come looking for me while I was otherwise engaged.
These are things I have encountered so far, and if I come across any others, I'll post them here. Does anyone else have a behavior related to movement or reaction to environment I didn't list here to add?