During the engine test scene, the pilot is helped into X-15, serial number 66671. When the test begins, the serial number is showing 66672.
At the beginning of the movie in a close-up side shot of the X-15 hanging under the B-52's wing, you can see that the cockpit cover on the X-15 is not fully seated in the closed position even though they are in a countdown to in-flight launch. A launch in that condition would have ripped the cockpit cover off of the aircraft and killed the pilot.