- Make sure there is a defined physical page for each navigation node term
- The terms must be available for tagging
- Make sure that anonymous users have read access to the TaxonomyHiddenList of the site-collection
- Always manage the navigation termset from site settings of the site-collection that hosts the termset; do not use manage term store from Central Admin
- If your custom code can't resolve and show terms in the navigation termset, make sure to use a view that don't depend on the cache being updated
Related to the managed navigation is the friendly URL (FURL) mechanism, which uses the term set structure to build the FURL from the linked-to term. To prevent broken links when moving a term, SP2013 stores links using the FIXUPREDIRECT.ASPX page, with params such as the termID, which will be resolved server-side into a friendly URL when rendered (see navigation term GetResolvedDisplayUrl). Do not render RichHtmlField using the simple "SPWC:FieldValue" web-control, as this will not resolve the fixup-links. In addition, having the same control both in an edit mode panel and in a display mode panel might cause problems.
This all applies to author-in-place (AIP) usage of term-driven navigation and friendly URLs; cross-site publishing (XSP) have different kind of issues.
Note that the managed navigation term set is stored in the default MMS of the hosting web-application. It uses the local term store for the site-collection it belongs to (IsSiteCollectionGroup). This will affect your backup/restore procedure as not only the content database or the site-collection backup will be needed for a restore, the MMS database or tenant backup is also needed. As all host-named site-collections (HNSC) share a web-application, restoring the MMS with it's term stores will affect the navigation term set of all site-collections. Take care.