I've recently been experimenting with the video feature of my D5200 and noticed this issue with the sharpness of the recordings:
2x video crop screenshot:
2x photo crop screenshot
As image width is limited on stackexchange you may want to look at the screenshots in an extra tab for the full resolution. Both shots were taken using the exact same camera settings. I scaled the photo to match the video and I don't think it was sharpened while downscaling. Oh and by the way, I am using the 40mbps firmware patch, but I don't think that should decrease video sharpness.
Has anybody got an idea why this is?