I was in the midst of writing up a feature-request to ask for a way to open the navigation menu from any screen rather than just the feed page. Getting around the app without one is hard. But lo and behold, while composing the post, I accidentally discovered that there is a drawer, on the left, displaying a list of notifications, and you open it by pulling from the edge towards the center. And sure enough, the navigation menu is where you'd expect, and it uses the standard gesture too. Great!
Except not that great. That gesture was the second thing I tried to open a nav menu; the first was looking for a button. I tried a couple times but wasn't successful, probably because I have a crummy screen protector which wrecks my precision. I spent over an hour searching meta and mucking about trying to figure this out before giving up.
If there were a visual indicator that these menus are present, it would have saved me time and frustration, and I expected the menu and gesture. A user who isn't familiar with android conventions would have a lot more trouble figuring it out.
I'm not sure what kind of indicator would be a good idea. When side pulling was introduced at a system level on the Galaxy S3, to open a drawer for context switching between apps, I tried it for five minutes then turned it off. I loved the functionality but hated that giant tab on the side of my screen.
But having something to train users about working the basic key elements of the app would be a big help. Perhaps some sort of tour, accessible from the nav drawer and on first launch?