The meta answer is CLASSIC (Hint: Find a seven-letter adjective.) Four of the Across answers start with an element on the periodic table:
17A. CHLORINETABLETS
19/34/39A. ARSENICANDOLDLACE
51A. SILICONVALLEY
55A. CARBONTAX
The name of the puzzle "Period Pieces," hints that the answer is made of "pieces" from the periodic table. Change each of those elements--chlorine, arsenic, silicon, and carbon--to their periodic table symbols--Cl, As, Si, and C, and you get the letters in the word CLASSIC, a seven-letter adjective that describes many period pieces (the other meaning of the puzzle's title) that satisfies the puzzle's hint.
Saw the periodic IDs almost immediately, actually saw too many (Boron, Silver, etc.) but them the actual elements were there and I saw immediately it was going to be a CLASSIC. Thanks Cory, that was FLUORINEDEFIENCY, URANIUMORE, NITROGENMUSTARD!