To the best of my knowledge, there is no known error in measuring gravitational time dilation. The phenomenon of gravitational time dilation is a well-established prediction of the theory of general relativity and has been experimentally confirmed to a high degree of precision.
Gravitational time dilation occurs due to the warping of spacetime caused by massive objects. The closer an object is to a massive body, such as a planet or a black hole, the stronger the gravitational field it experiences, and the slower time passes for it compared to a reference point further away from the gravitational source.
Experimental observations have supported the predictions of gravitational time dilation. For example, the famous Hafele-Keating experiment conducted in the 1970s involved comparing the timekeeping of atomic clocks aboard airplanes flying in opposite directions around the Earth. The experiment confirmed the relativistic effects of time dilation due to differences in gravitational potential and velocity.
Since then, numerous experiments and observations, including the use of highly precise atomic clocks in Earth's gravitational field, measurements of time dilation in satellite systems like the Global Positioning System (GPS), and studies of gravitational redshift, have consistently provided evidence supporting the validity of gravitational time dilation.
It's important to note that while our measurements and understanding of gravitational time dilation are highly accurate, there is always room for refinement and improvement as science progresses. However, there are no significant errors or challenges to the established measurements of gravitational time dilation.