The way to fix this, however it will screw with your calendar events and other minor issues, is to delete the settings database table. Create a backup of it first and all of your events, etc. Anything labeled ai1ec in the SQL needs to be backed up.
It removes the error completely, this means there is an issue with how their settings php and sql is coded and interacts with eachother. Other people reported disabling GZIP and other features fixes it.
The BEST fix option:
Delete the plugin directory, download the new calendar update from http://time.ly/ it is v 2.0.5 (at this time) and install and activate.
This fixed any issues I had with Arrays, etc. You have to replace your events most likely. I had a lot of errors with event posts.
