Was the regenerating tooth an error, or something else?

Don't expect an explanation:

The film’s final twist is the final freeze frame, a smiling Lockhart with all of his teeth intact. Verbinski has spoken about the film’s dream logic, that certain things are unknowable.

However, if you're interested in Dane DeHaan's opinion:

But I was curious if DeHaan had a theory about his character’s swift dental recovery?

“That’s the one thing in the movie I didn’t have to think about in terms of what it means, what it represents,” says DeHaan, “because it’s the end of the movie. Gore and I tried a couple different things, and I think it’s cool because it’s one last surprise, and it’s one last question, and it’s why the cure has side effects and will linger. And it will cause conversations, because [...] there is a surprise in this movie around every corner up until the very last second.”

My sense of the ending is that this isn't Lockhart, but in fact Dr. Volmer with Lockhart's face. Though a shovel was driven into his head and that he was "consumed" by the eels, the movie establishes that people of the Barron's bloodline aren't harmed by the eels. This is seen in the scene where Hannah menstruates into the pool, and attracts the eels without being attacked by them. Due to the cut scene, it is unclear whether Dr. Volmer had survived the incident, or what actually happened to Lockhart.

In the final scenes, the Lockhart in question looks at the burning sanitarium with some sort of familiarity in his face. The final menacing smile could be a subtle confirmation, that the Barron lives on after the destruction of Dr. Volmer and transformation into Lockhart.

So I am watching the movie again just for the sake of the broken/unbroken tooth. The point of change is not at the end of the movie but that was to get your attention, in case you missed it during the point when his missing tooth became whole again (on Netflix, it is at 2:04:38). Prior to that, example 1:59:22 where he was struggling with all the old people trying to pin him down, his missing tooth was very obvious. 1:59:51 where he is in the chamber, his mouth partially agape to show us the missing tooth. A lot of such scenes, if you are looking out for it, until the last one when his nose is pinched for him to open his mouth at 2:01:35 to go through the eel filtration process.

After this, he is seen sitting outside on a bench and Hannah comes to sit beside him. From this point onward, his teeth is whole again, giving you big smiles just to show you that he is cured after the eel filtration process. Yes, he opens his mouth quite a lot to show his whole set of teeth from here on quite a bit.

I don't believe the regenerating tooth was an error. As I understood it, Lockhart loses his first tooth as a result of the "treatment". When he goes into town and leaves Hannah at the bar, he speaks to the man who says his tooth loss is probably from severe dehydration (despite constantly drinking the water). We then see Lockhart trying and failing to uncover Dr Volmer's secrets and escape the facility. When we see him show off his new teeth, I understood that to mean the facility's dentist fixed them because Lockhart had given up resisting and accepted the treatment. He eventually snaps out of it, and you know the rest.

So how did the teeth and gums heal so quickly? I chalk that up to a little suspension of disbelief. I don't believe it was meant to imply the elixir has that kind of healing power, only life extension.