Connector structures for electronic devices may be provided with moisture indicators. The connector structures may include a connector such as data port connector that has a rear opening. A moisture barrier structure may cover the rear of the data port connector and may have an opening that is aligned with the rear opening. A moisture indicator may cover the opening in the moisture barrier structure. A transparent window structure such as a layer of clear film may be used to prevent moisture from traveling through the rear opening of the data port connector and the opening in the moisture barrier structure to the moisture indicator. An audio port connector may be provided with a moisture indicator and a transparent window structure that helps prevent moisture from reaching the moisture indicator through the audio port connector.