As the developer of JCH Optimize, from my experience, most of the problems people experience with the plugin is either from incorrectly configuring the plugin or errors on the website.
Every website is different so needs to configured individually so I strongly recommend reading the documentation and tutorials on how to configure and use the plugin before trying to install it on your live site, something a lot of people fail to do.
If you have errors in your javascript file or parsing errors in your css file, while they may seem to work well as individual files you WILL have trouble when these files are combined so it is best to check for these and correct them first. Check for javascript errors in your browser's javascript console and you can check for parsing errors in css using http://csslint.net/. Ignore errors about vendor specific rules like 'Unknown @ rule: @-ms-keyframes'.
However there is ample support and information on the website for users of the plugin at https://www.jch-optimize.net/. Subscribers can get premium support and assistance in configuring the plugin on your site so no need to post support requests on stackoverflow.
BTW the answer by itoctopus is incorrect. The plugin generates cache based on the name of the files or a hash of the content in inline styles/script, so any content generated on the fly will generate another cache. There's also a tutorial on the site that describes how to handle these kinds of situation to prevent excess cache from being generated. It would have served him well to read through the documentation before using.