Companions are a fun and interesting part of The Old Republic, especially when leveling. For the most part, the system Bioware has in place works pretty well. Here are some suggestions or tweaks that I think would improve companion gameplay.
1. If a quest rewards companion gear, give the gear for all the companions as a reward.
Right now, if a quest rewards companion gear, you have to pick one piece for one companion. This method strongly encourages the player to only gear up the current companion, while the other companions lag behind. As well, if your current companion doesn't need the gear, it's a bit of a hassle to figure out which companion needs the gear the most.
There's also some issues when you need a specific companion at certain times, and not keeping their gear up to date can make fights harder than they should be.
On the other hand, if you simply got gear for all your companions at the same time, it would make life a lot simpler. All your companions get upgrades, keeping their gear up to date, at least with green items. If a specific companion has better gear, you can just sell that companion's piece for a few credits. There's no, "oh, I made a mistake, I should have gotten Kaliyo's helmet instead of Vector's".
Plus, you get to see the changing looks for all your companions as you level. I think this would greatly simplify companion gearing while leveling, without really overpowering anything.
2. Rearrange companion ability bars so "stances" show up in the 4-button bar.
Right now, the default companion UI shows four buttons: Attack, Passive, and the first two abilities. The bar can be temporarily expanded to show all abilities, but it overlaps one of your regular bars. For some reason, you cannot rearrange companion abilities on the bar, though you can toggle abilities on or off.
Each companion also has two stances, like a DPS stance or a tank stance. Or single-target versus AoE. A lot of times these stances are on the very right.
It would make life a little easier if the stances were on the left, so they showed up in the small 4-button bar. Then that bar would be: Attack, Passive, Stance 1, Stance 2. This way you could more easily swap companion stances as appropriate.
3. Not use AoE when Crowd Control is active.
Right now, companions are very good with not interrupting crowd control when they use their single-target abilities. But if you enable AoE abilities, odds are that your crowd control will get broken by their AoE within seconds of applying it.
It is a significant hassle to keep expanding the companion ability bar and turn on and off AoE fight by fight. On all my characters, I've gotten into the habit of just turning all the AoE off. It's so much easier to use crowd control abilities when you're confident that the companion won't break them.
A simple rule where the companion simply doesn't use AoE abilities when any enemy is under a crowd control would go a long way towards making companion AoE abilities useful all the time. You could just enable the AoE abilities, and be confident that your crowd control is not going to be broken.
To be clear, I'm not asking that the companion calculate if its AoE will hit a crowd controlled enemy. That is probably excessive. A simple check if anything is controlled or not is enough, regardless of where the enemy is.
4. Integrate companions into the healing/operations UI.
It is extraordinarily annoying to try to heal someone else's companion. Especially in two person groups for the small heroics.
All I would like here is for companions to show up in the operations UI. That UI is the best for healing. Just have the companion health bar show up as if it was another player. All health bars are in one place, and healing companions becomes just like healing other players in the group.
5. Improve conditions when companions start attacking someone.
There are two situations I've encountered where the companion does not start attacking as you would expect. First, is Imperial Agent Sniper. For some reason, most of the main abilities used by the Sniper don't cause the companion to attack. But other abilities do. It would be a lot easier if all Sniper abilities caused the companion to attack.
The second situation is if you are the healer in a group. Your companion only attacks enemies which attack you, or which you attack. That means a lot of the time you have to micro-manage your companion to keep him attacking. Otherwise he might kill one enemy, then stop attacking and just stand there. It's very annoying when you are busy healing, especially as you are trying to fight the UI as described in point 4.
I would suggest that your companion starts attacking when anyone in your group attacks someone or when anyone in your group gets attacked. This would make managing your companion while healing a lot easier, as easy as it is when you are dealing damage or tanking.
For the most part, companions work well and are an enjoyable element of questing. But I think the five improvements above would smooth out a few of the rough edges of companion gameplay.