When I use AllVideos to load a mp4 file in an article, everything is OK, but if I try to use AllVideos in a Custom HTML mode displayed at home page, the plugin does not work.

Could not Allvideos plugin be used at Custom HTML modules?

Not sure what version of Joomla you are using, but in version 1.5 plugins in the Custom HTML module where not parsed so they would not show up.  I don't believe that has changed any in version 2.5. Perhaps something like this:

extensions.joomla.org/extensions/core-enhancements/coding-a-scripts-integration/custom-code-in-modules/16359

would help