Well, I am happy to announce I have solved the problem of getting 404 errors and my shopping cart and other pages not showing up because the URL ended in .html.
I was able to permanently remove the html extension by installing another plugin called, Permalinks Editor, which can be found here: http://wordpress.org/extend/plugins/permalink-editor/
After you install Permalinks Editor, there should be an option to change the permalinks. Go to admin --> page --> edit and then look for the "customize" button next to the permalink. Change that.
But then note, I found it necessary to deactivate the plugin and then reactivate it again for everything to work correctly.
Now, to answer your question gekkewaus, you could try uninstalling and reinstalling the plugin. Although, again, what I found is I had to deactivate and reactivate for many of the changes I made to actually work!
I did not actually uninstall/reinstall the plugin. I simply used the deactivate/reactivate option(s). Too often just updating did nothing. Not sure why. But that was my experience.
As far as the problem you are having, gekkewaus, I don't know if this is really going to help you. Your links don't appear to have .html at the end.
However, if I may so boldly suggest, you may want to customize your links. Make them "prettier" for SEO purposes.
So instead of http://firstclassverhuur.nl/?page_id=130, you could customize the URL to be http://firstclassverhuur.nl/fotogallerie
Just a suggestion. :-)
One more thing. You may find some help for your problem in other programming forums. I would think there are some in your country. I fancy http://forums.digitalpoint.com/forumdisplay.php?f=110. That's a link to the WordPress section of the Digital Point Forum.
If I find any answers for you, I'll come back and let you know.