Final answer:
The error in the sentence is the word "barrier's," which incorrectly uses an apostrophe to indicate a possessive form instead of the intended plural form. It should be corrected to "barriers."
Step-by-step explanation:
To find the one plural or possessive error in the sentence provided, it is important to look at the context in which nouns are used. The sentence is, "In 1972, President Nixon signed Title IX into law. One of this law's effects was to break down barrier's for female athletes."
The error in this sentence is the incorrect use of the apostrophe that makes "barrier's" possessive when it should be a plural noun. The correct form should be "barriers" as it refers to multiple obstacles or restrictions.