Yeah, he improvises all the time changing the music, altering the arrangements, and doing brand new lyrics to old songs, and the band adapts on the fly. You hear him do a song off the latest record and it's more likely to sound pretty much as it is on the recording, but even that isn't a certainty. The hardcore Dylan aficionados catalogue the lyrical changes on sites like expectingrain.com and you can find multiple versions of various older songs there.

I figure this keeps Bob from getting bored, it keeps the music fresh, and it makes the shows considerably more interesting than they might have been otherwise.

I'd have to say, though, that the very best shows I saw with Bob were in the 70s and 80s when he still had his whole vocal range, and he sang like a hurricane. I unfortunately didn't see any of his 60s concerts live. I wish I had.