So far, authorities re-examining the cases have identified at least 125 in which children allegedly were abused. No deaths have been connected to the lapses.
Gov. Jan Brewer has ordered an investigation.
Child welfare advocates said the Arizona debacle is not an isolated incident.
In North Carolina, a county social worker faces nearly four years in prison after pleading guilty to trying to cover up her agency's role after a child's death.
Prosecutors said that after the 2011 death of 15-month-old Aubrey Kina-Marie Littlejohn, social worker Candice Lassiter ordered a subordinate to falsify records to make it appear that the county Department of Social Services had done a thorough job investigating allegations that the girl had been abused.
An Associated Press investigation found that police and social workers were aware of reports that the child was being mistreated but failed to act in time.
Florida's Department of Children and Families has long been plagued by problems blamed on heavy caseloads, high staff turnover, lack of accountability and inadequate funding.
Last year, the agency overhauled its abuse hotline, which receives more than 400,000 calls a year, after problems were discovered in how information was collected and passed on to investigators.
Lawmakers there are still wrestling with how to fix the agency after the recent deaths of nine children monitored by DCF. The Florida agency's chief abruptly resigned in July.
The Michigan Human Services Department came under federal oversight in 2008 after it was accused of failing to protect children from abuse and neglect. A report last month by federal monitors found some improvements but noted that more needed to be done.
In Arizona, the number of abuse and neglect reports requiring investigation has risen 16 percent in the five years ending in March, according to the state Child Protective Services agency, while the number of children in foster care or other out-of-home oversight has surged from about 9,000 to nearly 15,000.
Meanwhile, the number of agency workers has remained essentially flat, with 20 percent annual turnover.
The 1,000 caseworkers assigned to child-welfare investigations have caseloads 77 percent above the standard, according to agency.