Here's what you can try, in the order that I would try them:
1) I don't think you have the latest stable release of FFmpeg. The top of your log file says:
FFmpeg version 0.6.5, Copyright (c) 2000-2010 the FFmpeg developers
I'm pretty sure the latest stable release of FFmpeg is at least into version 0.7.x, and the copyright reads 2000-2011? Try updating your FFmpeg to the latest stable
release, and see if that fixes your problems.
2) This line in the log file:
swScaler: Unknown format is not supported as input pixel format
...implies that the video track/stream of the video is encoded using a codec that FFmpeg doesn't recognize. And, in fact, the input video track/stream:
Stream #0.0(eng): Video: 0x0000, 1920x1080, PAR 1:1 DAR 16:9, 1k fps, 29.97 tbr, 1k tbn, 1k tbc
...doesn't even list a codec (that I can see). Kind of strange, since I assume YouTube generally re-encodes all videos that are uploaded to the site using some FFmpeg-compatible codec?
Does this happen for all YouTube videos, or do some YouTube videos convert OK (to video formats)?
3) The problem _might_ have something to do with this line in the log as well:
Seems stream 0 codec frame rate differs from container frame rate: 1000.00 (1000/1) -> 29.97 (30000/1001)
Perhaps FFmpeg is looking at the video container instead of the video track/stream (with regard to a video codec), and that's why FFmpeg can't find a video codec?
Sorry I can't give you a more cut-and-dry solution to your problem here. The truth is, I'm not really sure what the problem is just by looking at the log file. Try updating FFmpeg first, and then we can analyze subsequent log files if the problem persists.