Black bumps on the cut surface of an avocado
It looks to me (although I'd want to use a microscope to check) like the black dots are xylem. When you cut the fruit, you've severed the xylem and also exposed the flat surface. Three main things have then happened:


The increased surface area has led to the 'fleshy' part of the fruit contracting as the cells dehydrate.
The stiffer, lignified xylem tubes have retained their structure and have not contracted with the rest of the fruit, so they've become exposed. 
The exposed xylem have blackened due to oxidation - this eventually happens to all the flesh but, again speculating here, the oil in the fleshy tissue might protect it from oxidation longer than the exposed xylem which don't have the oil coating.