How can I fix a pager limited to 2 pages? The pager on the home page of my website is limited to 2 pages, ie the paging links are only for page 1 and 2 and both next and last point to page 2, but there are a lot more pages than that.

Is there some setting which controls this?
You can set items per page for the Home page at Configuration/System/Site information/FRONT PAGE as shown in following image:


  


And you can check also how many nodes you have promoted to the frontpage  at Admin/Content. So these two settings will allow you set all this. Hope this will work. 

Additional:

If you want more settings for the FrontPage, you can go to Admin/Structure/Views/ and you can see a view named FrontPage, that is by default disabled. But you can enable. And that view works as a FrontPage. So in views setting you can set as you want.