I'm looking for fun examples of why integrated testing is important
There are some real-world examples that had such dramatic consequences they are almost laughable:
This is a quite famous "textbook" example:
(One NASA subteam used imperial units, and another used metric, resulting in a satellite failing to enter orbit around Mars and instead burning up in its atmosphere. Oops.)
There are many images such as this depicting bridges built from both ends that don't meet in the middle, which are funny even though they're fake:
But sometimes it really happens. It isn't quite as dramatic since in reality they build all the piers before building the decking.
And of course, there's the Tacoma Narrows Bridge.
Seeing the dryer video reminded me of this. I don't have a picture but I have been to a movie theater where the automatic hand dryer is directly in front of the person, just slightly above the sink area (between the sink and the mirror). So right after you wash your hands, and there may still be soap bubbles/water in the sink, you go and put your hands under the dryer and all the sink's contents end up on your shirt/face! Oops!