The answers to the numbered clues are
1 No sweat = EASY 2 Be important = MATTER 2 Big Apple state = NEW YORK 3 Japanese beverage = SAKE 3 Word heard in court = ORDER 4 Evil clown in literature = IT 5 Book retailer now owned by Barnes and Noble = BORDERS 6 Worm on a line = BAIT 7 No Country For ___ Men = OLD 8 Adders, for example = SNAKES 9 Exchange = SWITCH 10 Bar topic = LAW 11 Objects used for climbing = LADDERS 11 It has black and white squares = CROSSWORD 13 Proverb = SAYING 14 2500 year old board game = GO 18 Dre and Seuss, for example = DOCTORS 19 Early birds? = EGGS 20 Understand = GET 24 ___ the gap = MIND
These can be joined into 10 pairs with a word indicating an operation (and, without, times, over) to get phrases fitting the 10 clues at the bottom. We then perform the arithmetic operation on the numbers, and convert the result to a letter alphanumerically:
NBC TV Show = LAW AND ORDER = 10+3 = M Be evident = GO WITHOUT SAYING = 14-13 = A Breakfast dish = EGGS OVER EASY = 19/1 = S Game that involves moving up and down = SNAKES AND LADDERS = 8+11 = S Famous puzzle = NEW YORK TIMES CROSSWORD = 2*11 = V Type of fraud = BAIT AND SWITCH = 6+9 = O By force of will = MIND OVER MATTER = 24/2 = L Nostalgic reasons = OLD TIMES SAKE = 7*3 = U Nobel Peace Prize winner = DOCTORS WITHOUT BORDERS = 18-5 = M Move on = GET OVER IT = 20/4 = E
The resulting message, MASS/VOLUME, clues the final answer DENSITY.