Oops
Gross mistakes are a different matter and not to be accounted for as uncertainties. So, simply to guard against gross mistakes, it is wise to make at least three tries at any measurement.
Making only one measurement means that a mistake could go completely unnoticed. If you make two measurements and they do not agree, you still may not know which is ‘wrong’. But if you make three measurements, and two agree with each other while the third is very different, then you could be suspicious about the third.
But uncertainty of measurement is not really about operator mistakes. There are other good reasons for repeating measurements many times.
It is important to know that errors can be random or systematic.
Random errors - repeating the measurement gives randomly different results, therefore, repeated measurements give a better estimate.
Systematic errors - the same influence affects the result for each of the repeated measurements (but you may not be able to tell), so you will not learn extra by repeating the result. Other methods are needed to estimate systematic uncertainty.
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