I have a GeForce 8600GT card and am using nvidia-340 drivers, version 340.101-0ubuntu0.16.10.1. Going into full screen mode results in a mode smaller than the displayed area, where the mouse can be used to scroll the screen viewport around. Returning from full screen mode does not reset things back to the desktop mode, and instead leaves it in the same mode. Both of these behaviours seem broken.
SDL 1 mode changes work. Also xrandr mode changes work. That's why I'm reporting this as an SDL 2 bug, not an nvidia-340 bug. Earlier I dealt with an nvidia-340 bug https://bugs.launchpad.net/ubuntu/+source/nvidia-graphics-drivers-340/+bug/1671920 but that is solved and I don't think that's why this is failing.
I'm attaching a small program which can be used to examine this behaviour. It can be built for SDL 1 and SDL 2 by supplying appropriate -I directory and -l libary, as in:
gcc -I/usr/include/SDL sdl_togglefullscreen.c -lSDL -o sdl_togglefullscreen1
gcc -I/usr/include/SDL2 sdl_togglefullscreen.c -lSDL2 -o sdl_togglefullscreen2
If reproducing this bug make sure xrandr is installed so you can go back to your desired resolution if SDL 2 fails to go back to it. Use something like xrandr --output DVI-I-2 --mode 1600x1200
ProblemType: Bug
DistroRelease: Ubuntu 16.10
Package: libsdl2-2.0-0 2.0.4+dfsg2-1ubuntu1
ProcVersionSignature: Ubuntu 4.8.0-41.44-generic 4.8.17
Uname: Linux 4.8.0-41-generic x86_64
ApportVersion: 2.20.3-0ubuntu8.2
Architecture: amd64
CurrentDesktop: XFCE
Date: Fri Mar 10 17:09:30 2017
SourcePackage: libsdl2
UpgradeStatus: Upgraded to yakkety on 2016-10-13 (148 days ago)
SDL 2 is able to go back to the proper desktop resolution when exiting full screen if and only if the top left corner of the current viewport is at the top left of the displayed area. In other words, if I don't scroll the viewport right or down by going to those edges with the mouse, or if I scroll it and then scroll back to the left and top limits, only then do I go back to the proper resolution in desktop mode.