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What practical problems do you think this could cause in specifying or measuring time?

The patriot missile system tended to miss due to numerical error accumulated due to using floats to count time.

http://www-users.math.umn.edu/~arnold//disasters/patriot.htm...

due to using floats

No they weren't using floats. The article you've linked to says this really clearly.

This calculation was performed using a 24 bit fixed point register

http://www.cs.unc.edu/~smp/COMP205/LECTURES/ERROR/lec23/node...

They meant fixed precision not fixed point math.

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