For the WordPress Media Gallery to work properly on a server, PHP Safe Mode must be turned off. From what I am told when PHP Safe mode is on, PHP runs as a different user than apache and this causes folder creation/modification problems. So for the uploader to work it must be turned off.
Also I have noticed some issue in the past with the flash uploader and it displaying HTTP Errors. I have found that if the server is protected by 401 Authentication this happens. I am sure that there are other problems that cause this, but this is the first fix I have found in my troubleshooting.