I had the same problem. The URL for the image that I was using was an absolute URL for another web site and the image would show up in the editor, but not in the final post.
The problem for me was that the "Text Format" was set to "Filtered HTML" instead of "Full HTML". From what I understand, "Filtered HTML" disallows the use of certain HTML tags.
NOTE: Permissions have to be set to use the "Full HTML" option. Although, an Administrator should be able to use it by default.
There is a page about the text formatting on the Drupal site:
http://drupal.org/node/213156
According to the page, disallowed tags should have been escaped (shown as HTML). Although, for me, they were removed. Also, I checked the "Configuration > Content authoring > Text formats" section and, for Drupal 7, it appears that IMG tags can be used, but there is a limit on how many characters are usable in an IMG tag.
I know this response is quite late, but it might be of help to other people having this problem.