My understanding is that most old NASA stuff is PD and free. So no problem there.
But recent missions have different image copyrights, mentioning universities, science teams, etc. And I'm under the impression that you must mention those every time you display the image....
An example regarding video:
Q: I want to use the footage in a YouTube video. Is it OK just to put the credit in the text description that appears next to the video?
A: No, as this is hidden inside a tab. Also it is not visible if the video is embedded in another website. Please include the full credit ‘burned in’ or overlaid on the video, or clearly visible as a credit at the end.