Can measurements taken from an ultrasound lead to a wrong estimation of gestational age?

Yes: An ultrasound done in the first trimester will be accurate to within a week of the due date. In fact don't think of it as a due date, but more as a due week as 90% of women will have their baby one week around their due date. Ultrasounds in the second and third trimester will be accurate to within 2-3 weeks of the due date.

Yes: The later the ultrasound is done, the less accurate it is for the estimation of gestational age. That is why gestational age is assigned based on the estimate for the first ultrasound. An ultrasound during the first trimester is probably within 2 weeks of the actual dates. Subsequent ultrasounds are used to evaluate adequacy of fetal growth as well as for anomaly scanning.