I was poking around and the issue is with
?show=slide that appears at the end of the url.
That is the bit of code NextGen uses to activate the slideshow.
Since you mentioned the slideshow works on other pages, it would appear the problem isn't necessarily with NextGen, but the theme/settings/etc.
Was there a time when the slideshow link worked on your front page? Or, is this a new site, and you've never had a working slideshow there?
Just a note, if you want an easy fix, just disable the slideshow link. No slideshows, but you won't have to chase down this error.
I just want to confirm, on the WordPress Settings->Reading page, do you have either:
- Latest Blog Posts
- A static page (select below)
checked. If static is checked, what pages have you selected in the two dropdown boxes. You shouldn't select the same page in both, it should give you a warning if you do. It can cause issues.
Also, what do you have selected in Settings->Permalinks? If your using a custom structure, what exactly is in the custom structure box?