Two of the critical areas that are emerging for me are rear mount escape and escape from the armlock from mount.
The emphasis is on "escape." I've gotten to the point where I can survive, for awhile if need be. But I have to be careful of becoming complacent in my ability to survive a triangle or choke attacks from rear mount. Theoretically, the more desperate my opponent becomes at my defense, the more I should be able to exploit that desperation with an escape rather than just more "defense."
For the rear mount escape, it's mostly a matter of getting back to basics: the scoop, the elbow kick and hipscape ... Tonight I spent a little time reviewing escapes for when you are late and the guy already has the collar from rear mount. Here, the idea is to look at the choking elbow and fall back on your side (almost as if doing a breakfall drill). You want your weight to be on the guy's leg just below the knee to effectively trap it. Also be careful of not falling flat on your back, making it easy to get mounted. To the side, to the side, to the side.
From there, you can pretty easily move your lower leg out from under the trapped/pinned leg. Then just back your way out of the rear mount.
As for the armlock from mount, this is one that Saulo outlines nicely in his book. Get him to fall for the deep elbow lock. Turn away to secure it. Then reach with your other hand to remove the lower leg from the face with a sort of figure four grip with your now-out-of-danger elbow-locked arm. You might have to hipscape back a bit to get an angle, but you want to sit up from here, folding his legs over and away to the side. Move toward the back (though he'll likely turn so that you end up in side control).