If you receive the error visible in the image below in the realtime stats view after the upgrade of your Joomla to the version 3.5, the problem is due to the database upgrade included in Joomla 3.5 and to the old MySQL version 5.1 running on your server.

To fix the issue you have to install the JRealtime Analytics package 3.0.1 or higher AFTER that you have upgraded to Joomla 3.5.

If you had previously installed JRealtime Analytics package 3.0.1 on Joomla 3.4 you have to reinstall it.

During the installation of the package 3.0.1 or higher the JRealtime database will be updated accordingly to the latest changes done in the Joomla 3.5 database for the new UTF8 standard.
After that the JRealtime will restart to work normally as before.