The puzzle answers are:
A Match Made In Heaven CHINSTRAP Ancient Riddles GUNDREMMINGEN Cheese Grater TABLOIDS Epic Rap Battles of Modern Art SPICING Hall of Mirrors UPWARD Lateral Thought GALLING O, the Anguish! GLADDEST Of Friends Grey and Quirks Typographical BANDAIDS Oh, What A (Double) Dummy I've Been! SEAN SOUTH Plot Points THINGS FALL APART Word Logic EXTRAPOLATING Zig Zag SUEDE VEST
These each have a string of letters in common with one of the words in the 12 Days of Christmas, one for each numbered day:
1: PEAR U(P[W]AR)D 2: DOVES SUE(D[E]VES)T 3: HENS C(H[I]NS)TRAP 4: CALLING ([G]ALLING) 5: RINGS T([H]INGS)FALLAPART 6: LAYING EXTRAPO(LA[T]ING) 7: SWANS (S[E]ANS)OUTH 8: MAIDS BAN([D]AIDS) 9: LADIES G(LAD[D]ES)T 10: LORDS TAB(LO[I]DS) 11: PIPING S(PI[C]ING) 12: DRUMMING GUN(DR[E]MMING)EN
The replacement letters in each answer word spell WEIGHTED DICE, the answer to the puzzle.