Was sent an image in an email today, was unable to see the image, just a broken container box, with a broken link icon inside and the URL of the source. The URL was not selectable, as swiping it caused the whole container to drag as an icon.
There was no "Show Remote Content" button as an option to view the image either, strangely.
I went into config editor and ensured that "permissions.default.image" was set to 1, per this page's discussion: http://kb.mozillazine.org/Privacy_basics_(Thunderbird) and I also set "mailnews.message_display.disable_remote_image" to true.
Neither presented the "Show Remote Content" button in Thunderbird v 24.6.0 on CentOS 6.5. It did work on Mom's Ubuntu 10.04 with Thunderbird v 24.5.0 though.
After much searching and even asking on irc://irc.mozilla.org/#thunderbird I found the answer, and it's a massive "Derp!"
On the menu bar, View / Message Body As / Original HTML, not View / Message Body As / Simple HTML.
Fixed it.
BTW, clued in to it by looking at the "view source" of the message and reading the HTML image include and alt text tags.
Also, I'm old-school enough to still believe in "Friends don't send friends HTML email," but I know I'm in a minority these days.