After posting earlier, I thought about it some. As far as party support Factotums, I feel like a melee battlefield controller (chain-tripper getting INT to the checks) should somehow be better on a factotum chassis than standard melees, but there's a logic leap I'm not quite making.
For night-at-the-improv bards, Bardic Knack plus Improvisation (fantastic level 1 spell from Spell Compendium!) should cover a lot. JaronK's right, though. Without Trapfinding, it can only go so far (I imagine there's a spell for that...).
I feel like the reverse is true; a bard is at its finest when he can whip out tons of spells (it's not his weak songs that make a vanilla bard 20 potent; it's their fantastic spell selection). Meanwhile, Inspiration points are per-encounter. They continue to contribute meaningfully throughout the day.