When bounty grace periods were introduced, Jeff commented:
I decided it can't hurt to extend the auto-award period 24 hours past the true end of the bounty.
There has now been time to observe how the grace period affects user behaviour:
without it, an offeror is implicitly encouraged to award her bounty to the first answer that satisfies its criteria (although she might hold off doing so until later in the bounty period, she must still proactively choose a deserving question knowing that others might yet follow); but
with it, I've more than once seen offerors say that whilst an answer is perfect they will hold-off awarding until the bounty has expired in case any better answers appear.
Whilst an undoubtedly minor point, such behaviour somewhat discourages (or at very least, does not promote) rapid answering of bounty questions—which would no doubt be better for both the questioner and the community (by "rapid" I do not mean hastily put-together sub-standard answers, as they are unlikely to have ever have been awarded the bounty); albeit that this effect is somewhat offset by the greater attention early answers will receive by virtue of being featured for longer and thereby may receive more upvotes.
It would be interesting to see some quantitative analysis of how the grace period has in fact changed behaviour (of both offerors and answerers); then consider whether grace periods are, in fact, more harmful than first thought.