[Moto X Q&A] tycoo:
Sorry for the late reply.

Yep, thats a good log.

Essentially these are the relevant lines (5769-5815):

E/mm-camera-intf( 268): mm_camera_open: opened, break out while loop
E/mm-camera-intf( 268): mm_camera_open: cannot open control fd of '/dev/video0' (Device or resource busy)
E/mm-camera-intf( 268): camera_open: mm_camera_open err = -1
E/QCameraHWI( 268): startCamera: cam_ops_open failed: id = 0
E/QCameraHWI( 268): mCamera handle or state is invalid mCameraHandle=0x0,camera state=0
E/QualcommCamera( 268): int android::camera_device_open(const hw_module_t*, const char*, hw_device_t**): end rc -1
I/CameraHalWatchdog( 268): Stopped Watchdog Thread...
E/CameraWrapper( 268): vendor camera open fail
E/CameraClient( 268): Could not open camera 0: -19
E/CameraClient( 268): initialize: Camera 0: unable to initialize device: No such device (-19)
I/CameraClient( 268): Destroying camera 0
E/CameraService( 268): connectFinishUnsafe: Could not initialize client from HAL module.
W/AudioFlinger( 268): session id 773 not found for pid 25210
W/AudioFlinger( 268): session id 774 not found for pid 25210
W/CameraBase(25210): An error occurred while connecting to camera: 0
W/ServiceManager( 268): Permission failure: android.permission.DUMP from uid=10091 pid=25550
W/OpenCameraCallable(25210): Exception in result (dur:212)
W/OpenCameraCallable(25210): com.motorola.camera.device.execption.CameraHardwareException: java.lang.RuntimeException: Fail to connect to camera service
W/OpenCameraCallable(25210):	at com.motorola.camera.device.callables.OpenCameraCallable.openCamera(OpenCameraCallable.java:133)
W/OpenCameraCallable(25210):	at com.motorola.camera.device.callables.OpenCameraCallable.call(OpenCameraCallable.java:62)
W/OpenCameraCallable(25210):	at com.motorola.camera.device.callables.CameraCallable.run(CameraCallable.java:47)
W/OpenCameraCallable(25210):	at com.motorola.camera.device.CameraService$2.handleMessage(CameraService.java:108)
W/OpenCameraCallable(25210):	at android.os.Handler.dispatchMessage(Handler.java:98)
W/OpenCameraCallable(25210):	at android.os.Looper.loop(Looper.java:135)
W/OpenCameraCallable(25210):	at android.os.HandlerThread.run(HandlerThread.java:61)
W/OpenCameraCallable(25210): Caused by: java.lang.RuntimeException: Fail to connect to camera service
W/OpenCameraCallable(25210):	at android.hardware.Camera.<init>(Camera.java:529)
W/OpenCameraCallable(25210):	at android.hardware.Camera.open(Camera.java:364)
W/OpenCameraCallable(25210):	at com.motorola.camera.device.callables.OpenCameraCallable.openCamera(OpenCameraCallable.java:169)
W/OpenCameraCallable(25210):	at com.motorola.camera.device.callables.OpenCameraCallable.openCamera(OpenCameraCallable.java:112)
W/OpenCameraCallable(25210):	... 6 more
W/ReadParamsCallable(25210): Exception in result (dur:1)
W/ReadParamsCallable(25210): java.lang.Exception: Camera isn't opened
W/ReadParamsCallable(25210):	at com.motorola.camera.device.callables.ReadParamsCallable.call(ReadParamsCallable.java:29)
W/ReadParamsCallable(25210):	at com.motorola.camera.device.callables.CameraCallable.run(CameraCallable.java:47)
W/ReadParamsCallable(25210):	at com.motorola.camera.device.CameraService$2.handleMessage(CameraService.java:108)
W/ReadParamsCallable(25210):	at android.os.Handler.dispatchMessage(Handler.java:98)
W/ReadParamsCallable(25210):	at android.os.Looper.loop(Looper.java:135)
W/ReadParamsCallable(25210):	at android.os.HandlerThread.run(HandlerThread.java:61)
W/SetParamsCallable(25210): Exception in result (dur:2)
W/SetParamsCallable(25210): java.lang.Exception: Camera isn't opened
W/SetParamsCallable(25210):	at com.motorola.camera.device.callables.SetParamsCallable.call(SetParamsCallable.java:58)
W/SetParamsCallable(25210):	at com.motorola.camera.device.callables.CameraCallable.run(CameraCallable.java:47)
W/SetParamsCallable(25210):	at com.motorola.camera.device.CameraService$2.handleMessage(CameraService.java:108)
W/SetParamsCallable(25210):	at android.os.Handler.dispatchMessage(Handler.java:98)
W/SetParamsCallable(25210):	at android.os.Looper.loop(Looper.java:135)
W/SetParamsCallable(25210):	at android.os.HandlerThread.run(HandlerThread.java:61)

Unfortunately now comes the hard part to understand the output.

Two thoughts. First, maybe it is worth to test the kernel i published in the android development section. I am not sure if it will fix the problem, though i merged some camera updates in there.

Second, as you had this problem with the stock rom too, in the worst case it may be a hardware error.

Btw, did you google and search around if this problem is maybe a common one and occured on other phones and roms too?