I have spent successive days 10-15 minutes at a time searching for how to make a bookmark in Repligo. A feature this basic and essential should be front-and-center in the interface.
Does anyone know how to do this?
When Repligo talks about "bookmarks", it does not mean the "paper clip to remember your last reading position". It rather speaks in terms of PDF specifics, where "bookmarks" are what is commonly referred to as "table of contents" (or in short: TOC), see RepliGo Reader for Android Features. And that's something the creator sets, not the reader.
But the same linked page gives you an idea for a work-around: You can use "annotations". This way you get a kind of "named bookmarks", which should be selectable like those "PDF bookmarks". I cannot say how exactly Repligo handles this, as I don't use it myself. It could very well be that it simply allows to add annotations, but doesn't keep an index for them. So in case you don't really need to change/edit things into the PDF, you might want to take a look at Moon+ Reader Pro for an alternative: This pro version also offers PDF support. And (at least with epub, what I mostly use) it handles bookmarks, annotations, highlights, and other whats-nots quite fine, including an index to look them up, and more.