1. Naming is pretty poor, same name for different potions with some differing effects is a little lame.
2. Alchemist not cited I noticed that crafters of weapons/armour get their name posted onto the items stats, I'm sure this could be done for potion 'sets' identical potions could just have multible names in the stats.
3. the ability to save a potion recipe would be cool, name it what you like even if it does just use an automated name when created, Currently I write down on paper my fav good potions.
4. Naming... cmon, we can report most other stuff if ppl abuse we can just report, I guess this one is a little, one way or the other for me, I can see the logic in having automated names, but maybe the ability for a user to right-click reset name could help if they don't like a personalised potion name.
5. MORE reagents... I know poisons are on the way, but man, 18 reagents is very small, things like persuasion need to make it in, the Mages guild has a passive for it, a potion like in other ES games needs to happen, I'm sure ZOS can come up with a heap more effects.
6. Enchantments, So you can't get any enchantment to enhance your proficiency in various areas?

Anyone else got anything else?
Alchemy feels half-done at this point, I hope it gets a good going over in the future.

Also, anyone notice that invisibility potions are set at 3 seconds on every level of alchemy? is this an error?