I get the message "Cannot Verify Server Identity. Wi-Fi can't verify the identity of '1.1.1.1'. Would you like to continue anyway?" It then gives me the choices "Cancel," "Details," and "Continue." But when I press any one of these nothing happens. I can't get rid of the screen. The slider doesn't work and using the iPad power off button doesn't resolve the issue.

The problem first arose after I went through the X-ray machine at an airport. At the time, I did not have the Airplane wireless off function activated, if that makes a difference. I am now at my destination (I am overseas) but the problem persists so it is not location-specific. Please help. Are there are any workarounds or so I have to take it to an Apple store?

You could try a soft reset. Hold down the power and home button until the Apple logo appears. The iPad should then reset. This will take a bit longer than restarting the iPad, so be patient.