It has been reported that the video of the A77 is actually crop because of the Steady Shot System (Sony's In-Body Stablization System).
There have been varying percentage of crop factor being reported ranging from 15% to 30%. I have emailed Sony Australia asking what is the exact crop factor on the video and I should get an answer within the week.
LesNumerique (a French website) has reported almost 30% crop factor
The video capture uses only 10,9x19,4 mm of a sensor measuring 15,7x23,7 mm : with the kit lens 16-50 mm, set at 24 mm we get 31 mm in video.
How would this affect your video; since the FOV (field of view) does not get refreshed until you hit the 'Movie Record' button then what your seeing on your EVF is not exactly the scene being captured.
The A77 is still the best APS-C DSLR on the market for doing video because of its AF Speed and Sony's Peaking Level.
NOTE: Apparently, the A33 does the same thing as stated on the Manual (page 81)
Looks like the Sony A55 is the only DSLT camera not doing any video crop...The angle of view of movies is narrower than that of still images. After you press the MOVIE button, the camera shows the actual range to be recorded (SLT-A33 only).