Parents are concerned that children who have trouble in school will 'fall through the cracks' in the school system. [=will not be given the help they need; will graduate without anyone noticing that they are unable to do the work]
The program is meant to help workers who may have 'slipped through the cracks' [=who may have not been included in other programs] because of their age.
You ought to 'get cracking' [='get going; get moving'] on that assignment. [=you should start working on that assignment right away]