- Inaccessible/invalid directory or subdirectory:
In some server configurations, manually(ftp or directly) created directories may not be writable by PHP(by IMCE). In this case, you have to set the chmod permissions of the directory to 0777 in order to make it writable by anyone.
You should also make sure that in each configuration profile all of the defined directories are located under drupal's file system path which is usually "files".
And also if "safe mode restriction" is active in your server, don't expect IMCE to run flawlessly.

- Disappearing images after node submission:
Having nothing to do with IMCE, it appeared many times in issue queues. This is an input filtering issue that can be resolved by adding tag into the default input format. Using Full HTML is another solution. See admin/settings/filters.

- Upload does not work in Opera:
Jquery form plugin before version 2.09 has problems with Opera 9.2+. Replace Drupal's misc/jquery.form.js with the one at http://jquery.malsup.com/form/#download

- IMCE may have problem working with Google Analytics and Secure pages modules. Just make sure to add imce* path to the exceptions list of these modules.

If you have another issue with IMCE, first of all, you should seek for a solution in the issue queue. In case you can't find any answer and think it is a new issue, post it to the issue queue providing detailed information.