[4] In late 2013, Gowan was one of a number of Republican lawmakers, represented by the Goldwater Institute who sued Governor Jan Brewer in an attempt to block the state's acceptance of Medicaid expansion under the Patient Protection and Affordable Care Act.

[4] During his tenure as Speaker, Gowan faced controversy including for spending House funds on redecorating.

[11] Gowan denied any intentional violation of the law, and repaid the state more than $12,000 after his use of travel funds was publicly reported.

[11] Gowan referred himself to the Arizona Attorney General's Office; in a memorandum released in 2017, the AG's Office decided not to pursue charges, concluding that although the "substantial disregard for determining whether state funds for per diem, mileage and official travel were paid pursuant to proper authority" was potentially a violation of state law, "the violations were not undertaken knowingly or intentionally but were instead attributable to negligence" and therefore did not meet the criminal intent standard for a prosecution.

The publisher of the Arizona Capitol Times suggested that Gowan's change in the rule was in retaliation for its investigative journalism.

[16] In 2021, Gowan sponsored legislation that would allow the Arizona state Legislature to override election results; he later dropped the bill.