There's an edge case in the GPS spec that only comes up every 20 years. It's well-documented and everything, but it only comes up every 20 years and software is terrible, so not every GPS unit is going to handle it well. Last time this happened, GPS wasn't nearly as widely used.

I would expect some percent of phones to flip out (try force restarting, or waiting a day and restarting). Which ones are a mystery - the GPS chip in a phone isn't even consistent for a particular model.

I wouldn't expect planes to fall out of the sky. I wouldn't be surprised by flight delays though; just because the safety critical stuff is well tested doesn't mean the rest is.

And the errors aren't going to be confined to April 6th. We're talking about software bugs here, and it's dealing with a number that counts in weeks. So while bugs should center on the 6th, anything within a week of that is pretty plausible too.

(I wrote the GPS tracking algorithm used for navigation in Google Maps. Nothing above is based on Google-specific knowledge. It's still just someone's opinion.)