Final answer:
The plural or possessive error in the sentence is the incorrect use of 'laws’' which should be corrected to 'law's' to properly denote singular possession.
Step-by-step explanation:
The error in the sentence 'In 1972, President Nixon signed Title IX into law. One of this laws’ effects was to break down barriers for female athletes' is in the possessive form 'laws’'. The correct possessive form for singular nouns should be 'law's' to denote that the effects belong to this one specific law. Therefore, the corrected sentence should read: 'In 1972, President Nixon signed Title IX into law. One of this law's effects was to break down barriers for female athletes.'