Could you send us some sort of screenshot or paste some HTML snippet from a content block that is rendered in IE but not in Firefox? It looks like an issue with Sitefinity itself and not with the migration tool, as the tool simply transfers the HTML content from 3.7 to 4.0. If you "view source" of your page in Firefox is the HTML code there but is simply invisible or it's not there at all?
There is an issue with the tool - it does not add view permissions for Everyone for the page controls, so unless you are currently logged in the backend you won't see the page controls in any browser. I suppose when you were testing with IE you were logged in the backed but you were not logged in Firefox. That's why you had the impression that your content was rendered in IE but not in FireFox.
A proper fix for the view permissions for Everyone should be uploaded in the next few days.
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