Tested this with current master but likely to be an issue on other stable versions.

If you're operating with a slow moodle site it is possible to add the same block multiple times. 

Instructions:

• Enable customization
• Click 'Add a block' 
• Click any option multiple times

Multiple blocks can also be added via the following:

1. Log in as an admin
2. On the dashboard, enable customisation and add a block(tested here with a calendar block)
3. Go to 'Site home' and add the same block from pt 2 and set it's visibility to be site wide.
4. Go back to dashboard and notice multiple calendar blocks exists on the dashboard.

 It must be noted here that in the test above the content of each calendar block differed(wrt events displayed) however on click of the month link both redirected to a calendar that shows the same content(i.e. the one added by the user initially).

However in some cases there are cases where we allow multiples(e.g. HTML blocks) but I couldn't find a place where the exact functionality is described concisely