Where will changes and fixes to guides and manuals for 5e be found? I'm interested in a grappler build, among others, and don't know where to look to see if the last bullet for the grappler feat has been changed. The grappler example aside, it should be useful to know for future fixes.
The most recent version of the Sage Advice Compendium will contain a list of links to errata for individual books
Wizards do not maintain a single up-to-date reference page which lists all the current errata or how to find it. However, their Sage Advice Compendium PDFs contain a list of links to the most recent (as of publishing) errata documents for all official 5e products; the best way to find errata is to check the most recent version of the SAC, revisions of which should be published in articles in the "Sage Advice" section of the WotC website.
As a general rule, most errata documents are announced/published in Sage Advice articles before being referenced in updates to Sage Advice Compendium, and those articles are not obviously updated when later errata affecting the same resources is published (though the files they link to may change to newer versions without notice). In some cases Wizards have announced new errata solely by announcing a new SAC version with the new links, as in the November 2020 update. The December 2021 update announced new errata while simultaneously linking to a new version of the SAC (and, despite calling it a Sage Advice article, didn't actually put it in the Sage Advice section of their site).
This all makes trying to search the internet for relevant errata quite annoying, especially as the order in which the articles are indexed by search engines does not necessarily put the most recent version at the top of the list.
(It must also be noted, as per Akixkisu's answer, that the official errata documents do not actually document all of the changes in text that have been introduced in newer printings of some 5e books, including changes that some consider significant.)
As of this edit, the most recent version of the Sage Advice Compendium is v2.7 (~December 2021), but this will undoubtedly be superseded in the future. The list of errata links from this version is reproduced below.
Errata have been issued for certain fifth edition books and can be downloaded at the following locations.
Dungeon Master’s Guide
Curse of Strahd
Eberron: Rising from the Last War
Ghosts of Saltmarsh
Hoard of the Dragon Queen
Mordenkainen's Tome of Foes
Out of the Abyss
Princes of the Apocalypse
Storm King’s Thunder
Sword Coast Adventurer’s Guide
Tales from the Yawning Portal
Tasha's Cauldron of Everything
Tomb of Annihilation
Volo’s Guide to Monsters
Xanathar's Guide to Everything
For those interested in reviewing the history of the SAC, the answers to this question include a list of links to archived versions of the SAC and some examination of the changes between them.
A set of errata for D&D 5e corebooks have been published, directly to a news article from which they can be downloaded: Errata for the Monster Manual and Dungeon Master's Guide. (Despite the name, the PHB errata can also be found there.) The direct link to the PDFs are here for the PHB, DMG, and MM. This article also contains a link to the Sage Advice Compendium and a few other resources specific to 5e--it's a good one to bookmark!
Along with this, the Basic 5e D&D pdfs have been updated which can be found at the D&D Basic Rules web site.
Several 5e designers have addressed rules questions over twitter—Jeremy Crawford, Mike Mearls, Chris Perkins and Rodney Thompson. However, Mearls stated in his reddit AMA that his answers are in his experience only and Crawford is the "official rules expert." Perkins also tweeted that Crawford is the "resident rules sage" and affirmed that Crawford provides the official answers. Crawford confirmed his "official" status in early November 2014, tweeting "Yeah, any official ruling is made or approved by me."
At this time (January 2015), 5e designer Jeremy Crawford is the official source for rules clarifications. Crawford and Perkins have tweeted about an official FAQ (initially slated for Fall 2014 release) and an upcoming 5e rules column on the Wizards website, although neither has materialized. The latest from Crawford is:
Errata documents are definitely on the way, starting with the Player's Handbook. They'll start coming out before the spring. / When I say "before the spring," that means spring is the latest you'll see it. / The errata documents will focus on corrections—adding any missing words and replacing or cutting incorrect ones—not on redesign. (Tweets, 22-24 Jan 2015)
The bullet simply shouldn't be there. It erroneously refers to an old version of the grappling rules.
That part of the feat is an error. It refers to a playtest version of the grappling rules.
WotC publishes errata in individual articles but compiles them in the Sage Advice Compendium
An easy to search Sage Advice Compendium is available on dndbeyond. This compendium accumulates the most recent ruling interpretations that WotC initially publishes in individual articles in the Sage Advice section of the WotC website. These articles are notoriously frustrating to search because they don't update with new errata releases, so the Sage Advice Compendium is, in most circumstances, your best option for the most recent changes.
The Sage Advice Compendium on dndbeyond is easy to browse due to the accessible handling of sections and the option to make direct links to it that don't require searches by other community members like the pdf version of the Sage Advice Compendium which links to all recent official errata - This link leads to the November 2020 version and it will not update to the newest version like the Sage Advice Compendium on dndbeyond upon a new compendium release.
For an exhaustive search and comparison of all communicated errata, you have no other option than to download all errata-pdfs in the Sage Advice section of the WotC website and to compare them manually. For an exhaustive search and comparison of all actual errata, you would have to compare all print editions by hand, manually - see this Q&A on 2018 PHB Errata.
The fan website www.SageAdvice.eu collects anecdotes and opinion by designers. It is not a collection of errata, and you should not refer to it as such.
Errata can be found on the WOTC D&D website under the Sage Advice section of the Articles tab. They produce a new article in this category every few months, as needed, and show links to information about other D&D reference stuff there.
Additionally, the unofficial and third party website www.sageadvice.eu website contains answers to rules questions that were asked of Mike Mearls and Jeremy Crawford. Crawford responses were originally considered Rules As Written and Rules As Intended, but this has changed over time and there is no official channel for rulings save the Errata as it is published. That said, Crawford is still one of the more respected voices for RAI within the D&D 5e community as the lead designer of the edition.