Even though it takes just a minor to drink the potion, shouldn't it at least take a minor to pull it out, and that's if the character has a free hand?
This would allow a player to pull it out one round and drink it the next, but by my understanding of the rules its not hugely faster than using ones second wind.
Dr. Ruminahui, shrink with a spear
Correct, but it's not quite as bad as that, since the PC can use his move action to take a minor action, so will generally be able to shift and use a healing potion, or attack and drink a potion. Quick Draw also works as mentioned.
Wizards, warlocks, archers and two-handed weapon fighters will often have a free hand. Some other characters can free a hand by dropping an off-hand item as a free action.