Why are some mounting holes connected to ground?
Connecting a metal chassis to ground obviously helps with shielding. For an analog circuit where sensitivity to noise and ground currents must be avoided, such as those dealing with audio or video, you are correct that to connecting at just one point is best. But for many cases (excuse the pun), it really doesn't matter as much. Further, if it is a circuit that handles power, connection to ground at many points serves both as a safety mechanism, and offers the advantage of spreading out larger currents over more board traces or ground plane areas. 

Your other question about proper physical mounting of multiple boards is mostly a design choice, and often more about convenience and fit then anything else, unless there are potential issues of EMI noise pickup between boards. But if you you are talking about multiple grounds, the same principals as the chassis discussion applies. If you are trying to distribute high current ground returns in multiple boards, you likely can connect each one to the chassis individually, at whatever point is convenient. But if there are many high sensitivity analog boards, you will likely do better to let only one main board make the chassis ground, and run grounds between boards separately and independently.

Finally, whether or not each ground needs to be run to a single point as opposed to nearest the circuit it connects to is something you'll get lots of opinions on, and no one choice is optimal in all cases.