I don't know how to fix Inkscape (I think the bug may be in Cairo rather than Inkscape itself), but I can tell you what's wrong with the EPS file.
There are many lines that look like this:
123.456 314.159 m f
(The numbers vary, of course, and sometimes there's a * at the end of the line.) This line adds an empty open subpath to the path before filling the path.
To fix the file, I removed everything from these lines except the final f (or f*),
I don't know how to fix Inkscape (I think the bug may be in Cairo rather than Inkscape itself), but I can tell you what's wrong with the EPS file.
There are many lines that look like this:
123.456 314.159 m f
(The numbers vary, of course, and sometimes there's a * at the end of the line.) This line adds an empty open subpath to the path before filling the path.
To fix the file, I removed everything from these lines except the final f (or f*),