With the rollout of Google’s mobile-first index, there are cases where desktop version will be indexed instead of the AMP version. One such case is that this happens is when there is no mobile version of your website. This would seem to be a rather rare case as Gary Illyes mentioned he has not seen this before. The primary reasoning for this seems to be because of the lack of navigation to other pages on that domain from AMPs.
After Sitelinks stop appearing in the SERPs just a couple weeks ago, they have made their triumphant return. While this didn’t affect brand searches, it did impact non brand queries. It appears as if this was more of a bug or issue on Google’s side instead of an intentional removal of the feature.
This article covers a few ways to get as many of your important site page’s crawled and indexed by search engine bots. This includes making it easy for a bot to crawl your site by doing some simple items such as; making sure all your pages are crawlable, there aren’t any broken links, and redirects are limited as much as possible. It also includes some more intensive pieces like having a clean sitemap feed, having the correct URL parameters and canonicals setup, and maintaining strong internal linking.