Here is the current info I have received from Nvidia tech support regarding the Experience 6 upgrade on the Shield TV in relation to the video stutter and audio/video being out of sync:
"We can clearly see the stuttering problem and this is consistent with what other users are reporting. We have been able to confirm the issue and development has root-caused the problem. The problem does appear to be specific to interlaced clips so far that we've been able to confirm.
I do believe you are also hitting another known but, and that is Plex auto refresh not working at times. This problem appears to occur when mixing HDMI 2.0/HDMI 1.4 devices. We are actively investigating this problem as well. I suspect if you manually change the SHIELD display resolution to sync with the video frame rate then you should not see the problem. In the case of the sample clip you provided it wad recorded at 23.976 FPS, so if the SHIELD display is set to 23/24 Hz then you shouldn't see the problem.
Again we are actively working on this issue and hope to provide a fix in a future update. In the meantime try manually changing your SHIELD display refresh rate to match the frame rate of the content and see if that helps. You can change the refresh rate from Settings > Display & sound.
We do believe the stuttering and audio/video sync issue are related so hopefully the fix will resolved both. The other issue with Plex auto refresh not working due to mixed HDMI 2.0/HDMI 1.4 is also something we are actively investigating."
Hopefully they get this squared away quickly and issue a fix for all of us Shield TV users