Chrome's new bookmark manager is definitely a poster child for "half-ass it then push it to the masses". It seems to be working hard to almost replicate the Windows 8.0 Metro interface that everyone loved down to the "checkmark a tile to open the menu".
If you want to make a new folder, go to the folder you want it to be in and press the NEW button on the left outside of the folders, there's no button for it on the right inside the folder (but there is a button to delete the entire folder from inside the folder).
If you want to drag items into your new folder, drop them quick. If you hesitate Chrome decides that you are re-ordering the items and you want the bookmark to go before the folder even though your mouse is directly over the tile.
If you have nested folders, opening a subfolder seems to randomly display all the elements in the center of the screen where you can't click on anything because its all on top of each other. Sometimes. There's no tree view of nested folders. Top level folders are on the left, after that you have to drill down individually.
No right clicking. Haven't you heard that there's no way to right click on a tablet?
When you checkmark a folder you don't get the option to edit its name or description. You have to open the folder then rename it from the inside.