Actually you have a number of issues here.
1 - For some reason, you're using https:// for a lot of your links. You only need to be using http:// for your links. This just creates confusion for your viewer as it means you're going from normal security to secure in a visitor's browsers and that usually kicks out a warning for them. They might not like that or understand it.
2 - If you look at your links, the broken ones are links to where you've told WordPress to 'link to a page' when you first wrote the article. An example I did with one of your pictures is here. Note when you click on the bookcover, it leads you to a Post with the, in this case smaller, image within the theme. If you click again, it then leads you to the full size picture.
Somehow, you've deleted these Posts. Not sure how you did it actually since these Posts don't show up on your Dashboard -> Manage -> Manage Posts page. Using my example, I don't see Post #2704. It's just used internally.
Best bet would be to just go back through and directly link to the image like it is with the other pictures in the Post.
Hope this helps,