A little background on what we are doing first. We are running several applications from a CLI, and not all of them are fully functional. They do on occasion core dump, not a problem. We are running a service that takes a screen scrape of those apps and displays them in a more user friendly Java window.
I have a Samsung gs3 gt 19300 running on cyanogen mod 10.2 stable version, so far it has been smooth other than the ram problem (which I also encounter when using stock ROM)
Whenever I restart, I often have around 300 + MB of free ram (after recent apps are all cleared) however, a few days later, I find that my free ram drops to less than 100 MB (with all recent apps cleared as well)
When you shut down a windows computer, it gets faster (if it's been on for a while). I notice that most, if not all, linux distros gain nearly nothing from restarts. In fact, I was actually suggested to restart my server (running Debian, a Linux OS) as little as possible in this serverfault question.