The Times was a bit imprecise in how they used the kid's words to explain the bug (about par for their technical reporting, unfortunately). The way they write it, it sounds a lot like <textarea maxlength=1000></textarea>, but if you think more about the explanation of the wide characters and the "print preview" it can't be that.
Overflow issues are actually not trivial to fix, as opposed to the claims some people are making here about "just count the words". Without allowing an excessive amount of space or allowing for more flexibility in the way it lays it out (flowing across multiple pages, etc.), it can be hard to estimate how much space to give for something as vague as a 150-word limit. If the Common App instead specified a 1000-character limit, the programmer/designer could take the widest character like "W" and determine the max y-height for 1000 W's.