My dad has a lung nodule that has been stable for 5 years. This year the CT scan showed it grew 1mm. Can CT measurements be wrong?

Yes, it is not exact. Growing lung nodules can be cancer. But the growth has to be real which means increase of more than 2-3 mm before we can get concerned. The cross sections on ct are rarely at the same level so there is one or 2 mm variation between serially done ct scans.
Yes. Ct measurements are 2 dimensional measurements of 3 dimensional objects so depending on how you choose to measure an irregularly shaped nodule will alter the resulting measurement. A 1mm change is probably within the allowed "error of measurement" for the test meaning that the test may be wrong about such a small change. At 5 mm the nodule can still be watched for growth with a later ct scan.