Mine kind of shudders at low idle sometimes too. As for stalling it, I have to admit that I'm ever so slightly out of practice. My last manual transmission daily driver was my '90 4Runner nine years ago (R.I.P.). But it's always been like riding a bike for me. I've always jumped right back into driving a stick whenever I've had the opportunity.
I stalled my Corolla twice just today -- and not the typical starting on a hill pressure situations, but just not paying enough attention. And that's the thing that bugs me. Driving a stick was second nature to me for many, many years. I'm not supposed to have to think about it.
I think the culprit is the drive-by-wire throttle. The engine doesn't quite spin up as quickly as my internal timer thinks it will and I end up with too much clutch and too little throttle. It doesn't chatter and get jerky, but it either dies or I catch it and put my right foot down and save it.
Try this some time if you have a long hill to go down: Get going down the hill in gear up to 60 or 70 MPH, take your foot off the accelerator, watch the tach, and drop it into neutral. It doesn't drop quickly or evenly from 3k RPM to idle. I think they've programmed the computer to anticipate that you're going to go to another gear and it keeps the RPMs up in a range near what might be needed for another gear. Mine drops down to 2k RPM almost right away, and then hovers for a split second before slowly dropping some more and then finally decides that you wanted idle after all.
The other thing I've noticed is that the accelerator lags on gear changes. Normally you start to back off the throttle just a little before putting the clutch in if you're trying for a smooth-feeling shift. Unless I back off earlier than my years of experience say I need to back off, the engine revs a little over where it was running when I put the clutch in even though I was backing off the throttle. I always thought that was something that n00bs did when they were first learning, but it's happening to me unless I think about it start backing off earlier than I normally would.
I think the drive-by-wire throttle is trying to do some of our thinking and driving for us. If they'd just rigged it to communicate the throttle position immediately and accurately (which I'm quite sure is possible), it would be a good system.
That's my story and I'm stickin' to it.