One of our students was having problems finding why some images were visible on her site and others weren't. There's no one-size-fits-all answer to this problem, but here is one way to start closing in on the answer.
Install the Web Developer Toolbar for Firefox
If you haven't done so already, install Firefox on your computer. You can download it from http://www.mozilla.com/firefox/
Then, with Firefox open, search Google for "webdeveloper toolbar".
Click "Add to Firefox" and you'll be able install the Web Developer toolbar. It will look like the image below.
Troubleshooting Your Site
The image above is a sample Drupal node. It is meant to have two images but one is missing. Here's how we'd start to look for the error:
Click "Images" and then "Find Broken Images". You'll see a result like the one below:
In this case the problem is obvious - I've written http://drul.org instead of http://drupal.org. However if your problem is more difficult, this technique will still tell you where Drupal is looking for the file and hopefully it will give you enough hints to fix the problem.