In Spanning Tree Protocol (STP), a layer-2 switching network can have multiple designated switches, as each segment can have its own designated switch. Thus, the statement that a layer-2 switching network can have only one designated switch is incorrect. Additionally, the switch with the smallest priority value is elected as the root switch, not a non-root switch. Hence, the statement that the switch with the smallest priority value is elected as a non-root switch is incorrect.