For multiple checkboxes issues in Joomla. If you are facing any problem like this you can solve it by following instruction:
in libraries/joomla/form/fields/checkboxes.php
line line 67:
need to change this two lines
$values = (is_array($this->value)) ? (array) $this->value : explode(",",$this->value);
$checked = (in_array((string) $option->value, $values) ? ' checked="checked"' : '');
You can check joomlacode.org.
http://joomlacode.org/gf/project/joomla/tracker/?action=TrackerItemEdit&tracker_item_id=28640