Actually, the glitch hillsboroks reports happens for me on the laptop as well: clicking on the 'heads' takes you to book view, but you still have to tap again on the 'Bookshelves' tab to see the members who have that book. Same is true for the stylized balloon that shows how many notes have been made on the book and its recipes -- clicking takes you to book view, where you then click on the 'Notes' tab. I'm honestly not sure whether this used to be a one-click process or not...
The 'chain' icon displays the linked books, and clicking it again toggles back to not showing them, and the 'plus' icon takes you directly to the dropdown list for adding a bookmark.
While we're talking about extra clicks, I would like to express a preference: in the previous version, when I clicked the 'plus' symbol to add a Bookmark, the drop-down dialog would appear, and I could immediately type the letter that the Bookmark begins with to be into the list. Now I have to click the down arrow to enter that list, and it's a (minor) pain, as I'm a keyboard-focused user, and have to take my hands off the keyboard to use the mouse or touchpad to take care of the down arrow.
Likewise, once I've highlighted a Bookmark in the list that I want to select, I'd like to be able to do so by hitting 'Enter' to apply it, rather than having to click the 'Save' button. Hitting the escape key makes the dialog box go away; hitting 'Enter' should apply the highlighted Bookmark. [To be clear, the enter-save feature is something I've asked for previously, but the having-to-hit-the-down-arrow in the dialog box is actually new with this version, so a step backward for the keyboard-centric.]