Solution of Magento Common Errors

CMS: Upload Image icon doesn't show up when clicking Insert a Image icon

Since uploading image needs the permission of Media Gallery, so we need to add this permission to the user which was used to manage CMS system in order for the user to have the ability to upload and insert images.

CMS: The directory is not writable by the server

The error might occur when trying to upload images in CMS. 

The reason is that CMS is trying to upload images to media/wysiwyg folder, but the folder was not created when Magento installed. Therefore, what we need to do is just to create the folder and make sure nginx/php user has the permission of it.

Magento Connect: 404 Not found

I got some answers from the internet which were all about the permission of downloader/index.php and some folders. You can clear cache using magento-clear-cache.php.
However, the cause of my issue is that the configuration of Ngninx. In my configuration I didn't rewrite dowloader/ to dowloader/index.php which might be a common mistake if nginx is used as PHP server, because .htaccess file which is doing the rewrite in Magento won't take effect under nginx.
To figure out whether this is the one causing your 404, you just need to put index.php manually after downloader URL to see whether it will work or not. If it works, then you have the same issue as mine.
To solve the issue, you just need to adjust the nginx configuration to make the rewrite also worked for downloader folder.