As far as I know, WotC has only ever released errata'd core rulebooks as deluxe editions. With 3.5, they had faux leather covers and bookmarks and such. The PHB had almost all the errata - and the deluxe edition ended up getting reprinted with the regular cover, as that is what I have - while the DMG and the MM had all their respective errata. With 4e, I believe they also released deluxe editions with silvery sort of covers that also incorporated all the errata for those books up to that point, but I could be wrong about that.
As WotC has not even published errata for 5e yet, I would not expect to see updated books any time soon. Some of the later printings might have fixes for minor typos (like the misspelling of aarakocra in the MM) but not any proper rules errata. I know that they are compiling lists of errors (like the fact that the warhorse stats in the PHB and MM don't include the horse's proficiency bonus in the hoof attack modifier), and they've said they will put out a survey to gauge how people are playing the game at some stage this year. They've also said that they will see people's opinions about rules they've identified as problematic before they officially change them.
So again, I wouldn't expect to see any official errata - at least not anything major - any time soon, and even then, I'm not entirely sure it will get incorporated into the next printing of the books. Based on past experience, it seems likely they may reserve incorporating errata into the core books for another deluxe edition.