Taliesin:
AFAIK nothing in the text implies that a later smite would end a previous smite. You should be fine.
That's how I'm reading it as well. It's important, because it will influence my first action.
@Puck Smite Evil gives me a buff to attack/damage and to my AC vs the target until they are dead or the following day when I regain my daily uses of the ability. But nothing in the ability says only 1 target can have smite evil active on them or not, which is why I was curious about it. But for example, it doesn't mention target limitation in the way that the Ranger's Quarry ability does, so I think as long as I have uses of it, I should hypothetically speaking be able to smite both of these baddies, but just in different rounds since it does require a swift action for me to smite them.
@Gorum -- I'm also trying to understand whether smiting someone will break my invisibility if I don't follow up with an attack? Rules around invisibility call attacks and spells that target a foe, but Smite is neither? Could I get an official ruling on this?
Based on that, I can either drink a pot, smite GK and move into position while still invisible and wait for the surprise attack next round after smiting Lady Ghast over there. Or if I become visible due to smiting, I'll have to rethink drinking the potion and just moving into position, smiting followed up by an attack on whoever I can reach of these two.