I have figured out a few things about this issue.
When you export the movie from QuickTime Player 10 with "Save for Web", a folder is created with a number of files and folders.
In the included ReadMe.html file you will find instructions how to insert code for using a JavaScript movie controller, or the original QuickTime movie controller. The code is slightly different for the two.
If you choose the JavaScript Controller AND do not copy the folders“scripts” and “stylesheets” into the same folder where your html file as well as the movie source and reference, and poster image files are located, you will not see the “Click to Play” button at all. When you click on the poster image for the movie, the movie will play just fine, but in a new web page with a name like ****.mov.
When you then copy the “scripts” and “stylesheets” folders into that same folder, the “Click to Play” button is now where it is supposed to be, but the location indicator on the timeline is in the wrong place, and when you click on the button or the “play” button, the screen goes blank in Firefox (Mac) and does not play, but the movie plays in Safari (Mac). The location indicator on the timeline is still in the wrong place. See http://www.abrasha.com/misc/test3
When you choose the QuickTime Controller, AND do not copy the folders “scripts” and “stylesheets” into the same folder where all the required files are located, you will again not see the “Click to Play” button, and everything else is the same as before.
When you then copy the “scripts” and “stylesheets” folders into that same folder, the “Click to Play” button is now again where it is supposed to be, but now there is a whole new issue. Everything is fine in Safari (Mac), but in Firefox (Mac) as soon as you click the Click to Play button the poster image changes to a gray field with a large X on it, and the browser cannot find the movie file. The movie will not play. See http://www.abrasha.com/misc/test4
So for now, until I can get Firefox to behave like I want it to, I will keep my videos without the Click to Play button. That way, they will at least play in both browsers.