There are a few issues that could cause this.

Thunderbird blocks all remote images by default. You can enable remote images for an email address by clicking on "Click here to always load remote images from ...". If you see this box in your message, you have to click it for each user that you want to see images from.

If you don't see this box, then there is another fix to try.

Thanks for the suggestion, but the box mentioned doesn't drop down for the messages without picture loading. I'm certain I have earlier changed the default to receive media from these people. What other fix is possible?

Here is another suggestion.

If you can never see remote images because the "Show Remote Images" button is always missing check that permissions.default.image is set to 1 using the config editor. It was here that I saw it:

http://kb.mozillazine.org/Privacy_basics_%28Thunderbird%29

This has worked for another person. It seems a bit involved but take your time and do what it says.

When I receive a message with the photos replaced by boxes with a little icon in the corner clicking on the option of displaying the remote images in this message does not result in their being displayded