So I've attached pictures so you can see what I mean. Basically when I export out to Business Catalyst, the slideshow refuses to be responsive to browser width. It looks like it tries to (image gets bigger as browser window gets bigger) but whatever it's encased in is set to follow the left side of the browser and isn't width responsive. This is just the basic slideshow widget that is built into Muse, no fancy 3rd party widgets.
Apologize for your frustration. This issue has been fixed in the pre-release build.
I suggest downloading our prerelease build http://adobe.ly/2cX7wIN and letting the team know of your observations in the prerelease forum.
If you have a backup copy of your files, you can continue using them by installing a previous version of Muse https://adobe.ly/2wMSxNv.