Does the phrase "I'll show you" also have a predefined special meaning? He seems to repeat it quite often.

I heard that as "I show you xx". One guy is flying with his head up, the other one talking most is monitoring with his head in the instruments, and helping the pilot flying getting confident data.

Remember they're driving 1970's technology, redundant everything, and they all grew up flying "steam gauges", where the culture includes tapping on the glass to make sure the needle didn't stick. They want to compare every sensor output for sanity so they can disregard one if needed.

This vid is also the source of cockpit audio for the FSim shuttle simulator game if you like this stuff.

So "I show you X" stands for "I see X on the instruments" (as opposed to just stating X as a fact)?

Yeah. Oh and Houston did the same thing, calling out the 180 and the 90 on the HAC - heading alignment circle. Just helping them out with their radar indication.

PS - here's what happens when they got a bad instrument and didn't catch it: http://www.avweb.com/news/safety/183035-1.html

What an awesome video; saving for future reference. We have much to learn from this in IT.