The only downsides: one or two cases of stardate overlap in the early episodes (mainly, "Miri" vs. "Dagger of the Mind", but Kirk may have been too consumed by the illness to get the last stardate right in "Miri"...), and then a problem that doesn't go away even with the extra years allowed by the stardates.
That problem is from the stardate-free "Day of the Dove", where Klingons think they have upheld the peace signed after "Errand of Mercy" for three years. It's not even two between the airdates of the episodes, so one'd think the stardate model would bring some relief here. Alas, "Errand" has a stardate of about 3200, so "Day of the Dove" ought to take place around SD 6200. Which isn't impossible by any means, but a bit annoying, when the stardate order would otherwise have TOS end with a bang - the supernova explosion of "All Our Yesterdays".