Outlook 2013 Issues. Surprise, surprise, but...

Outlook uses the same rendering engine as MS Word. This means it paints the page differently than a web browser. Those differences are then affected by a number of factors. Without all of the context or a screen recording, it’s difficult to troubleshoot. Some example assumptions:

Here, open could mean viewed in preview pane, or opened in new message window (where the email is re-painted).
In Outlook (all Windows versions), images are off by default, so unless the image and it's containing <td> have a width and height defined (by attributes or CSS), the entire email will be re-painted once they load.
Link status might be tested by hovering over an image and observing pointer cursor (which could be affected by CSS or rendering time), or by clicking on the item.
The image(s) in question my be linked in their entirety by being with an anchor, or may have an image map with an area tag.
There may also be FOUT (flash of unstyled text) due to the font stack, causing the email to be rendered twice on each open.
The active memory use of Outlook may be high and causing performance (and screen painting) lag.

Any or all of the above or yet some other factor may be at play here.
The good news is that all versions of Outlook combined only account for ~9% of all email opens, and your links seem to work some of the time.

I hope something here helps you troubleshoot.