Originally Posted by NoWhErE

go to this page : /wp-admin/edit-tags.php?taxonomy=category (your categories page)

at the top of the screen, hit the drop down menu (Screen Options). There you,ll see the option of how many categories to display on screen at once. Change the value to 100 or something higher.

Then just check the select all checkbox right beside the NAME column and apply the delete action.

Should take you about 30 seconds to go through 1500 categories IF you don't have to pick and choose which ones you want to keep.