If you upload a video through the Media Web Part it displays a default generic image of a film reel. Is it possible to have the default image be a snapshot of the video a few seconds in, similar to what YouTube does?
It's very easy to set the preview image of the Media Web Part via the
PreviewImageSource (see walkthrough here) property. In a solution I developed I let the customer upload a custom prevew image together with the video which would serve as preview image.
I think what you are asking to have this process automated, so the preview image is automatically filled with the frame at second X, correct? This is not possible out of the box. As suggested in the comment by PirateEric you might want to try the Podcasting Kit for SharePOint just to see how they are doing it there, but only use it for trying because besides that functionality it installs a lot of bloat.
You basically would need a framegrab of the video at a specific frame. You can check posts for framegrabbing here and here, but I don't think this is an easy quest as the Media WebPart only supports a few file formats/encodings. Maybe there are better media Web Parts out there which do this automatically for you?