[pplucky]

Firstly, switching to 3D mode only works when you have "Adjust display refresh rate to match video" enabled.

This did the trick for auto switch to 3D mode, but now the movie shows huge bars up and above, cutting part of the movie!
You can check here how it looks.

If I put "Adjust display refresh rate to match video" to "Off", it goes back to normal (showing 2 pictures SBS by default, but no cuts).
You can check here how it looks.

Enabling 3D mode manually also doesn't cut.

Subtitles seem to show OK with "Adjust display refresh rate to match video" at "On start/stop", but with huge characters (bigger than in normal mode).

Also can you (ssh in and) run
tvservice -s
before starting the video,

Code:

state 0x12001a [HDMI CEA (16) RGB lim 16:9], 1920x1080 @ 60Hz, progressive

and then again when video is playing.

Code:

state 0x12001a [HDMI CEA (31) 3D SbS RGB lim 16:9], 1920x1080 @ 50Hz, progressive

Also what does
tvservice -m CEA
return?

Code:

Group CEA has 14 modes:
           mode 1: 640x480 @ 60Hz 4:3, clock:25MHz  progressive
           mode 2: 720x480 @ 60Hz 4:3, clock:27MHz  progressive
           mode 3: 720x480 @ 60Hz 16:9, clock:27MHz  progressive
           mode 4: 1280x720 @ 60Hz 16:9, clock:74MHz  progressive 3D:TopBot|SbS-HH
           mode 5: 1920x1080 @ 60Hz 16:9, clock:74MHz  interlaced 3D:TopBot|SbS-HH
  (native) mode 16: 1920x1080 @ 60Hz 16:9, clock:148MHz  progressive 3D:TopBot|SbS-HH
           mode 17: 720x576 @ 50Hz 4:3, clock:27MHz  progressive
           mode 18: 720x576 @ 50Hz 16:9, clock:27MHz  progressive
           mode 19: 1280x720 @ 50Hz 16:9, clock:74MHz  progressive 3D:TopBot|SbS-HH
           mode 20: 1920x1080 @ 50Hz 16:9, clock:74MHz  interlaced 3D:TopBot|SbS-HH
           mode 31: 1920x1080 @ 50Hz 16:9, clock:148MHz  progressive 3D:TopBot|SbS-HH
           mode 32: 1920x1080 @ 24Hz 16:9, clock:74MHz  progressive 3D:TopBot|SbS-HH
           mode 33: 1920x1080 @ 25Hz 16:9, clock:74MHz  progressive 3D:TopBot|SbS-HH
           mode 34: 1920x1080 @ 30Hz 16:9, clock:74MHz  progressive 3D:TopBot|SbS-HH