Annotation - The ability to mark up hypertext... yeah... HTML claims to do it, but you can't change a document once it's read only. You should be able to layer annotations on top of a document. HTML simply is not a Language for the Markup of Hypertext Documents.
[Edit/Extend] - Annotation is anything you could do with a printout, at minimum. Circle something, highlight a section, black something out, attach links, etc. It's not just tagging a file as a black box.
Trails - the ability to store a trail of annotations, linking up parts of two documents together, or more. Like a stack of bookmarks, except bookmarks can't anchor to part of a document.
Publication - One of the crucial features of the Memex was the ability to output a collection to allow sharing with others. It could spit out a copy of everything linked to a trail, all the files, all in one dump. Copyright holders would have a huge problem with Memex if it were implemented as originally shown.
I think it should be possible to build a proxy that records ALL local http(s) traffic, and thus record all the sources to documents you've seen... and then only keep those that you've tagged or linked to after a few months, purging the rest. A private Memex, but it couldn't even be an open source project, as copyright holders would work to squash it.