I am facing the same error. There is a ‘#’ missing in the URL when the images change.
Here is an example in my site.
Carousel
If you try to move to the next image, the url appears as: “domain/post/jp-carousel-99” instead of “domain/post/#jp-carousel-99” causing the 404 error.
Oh and if you hit the Back button, the carousel is loaded again with the next image as it was supposed to.
I hope this is exactly the same error that Josh is reporting.
Thanks!