Not really menus, but related to the “programmability” of DVDs, my “favourite” “feature” was unskippable videos which would show before the feature.

This was used to reward people who had actually paid for the movie with being forced to endure obnoxious and long “you wouldn’t steal a car” anti-piracy appeals before they could watch the main feature.

An interesting effect of them doing this is that it made the pirated version of the product objectively better than the legal version. Great thinking by movie studios.