With probability sampling you have no control over the units that are sampled. So the only way to reduce the margin of error is to increase the size of the sample.
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Sampling errors are errors in the data collected during the carrying out of quantitative data surveys. They can occur for various reasons, e.g. surveys that were incorrectly filled out. It is generally said that a survey needs to have a margin of error of under 3% to be statistically significant.
It depends on whether it is the Type I Error or the Type II Error that is increased.
Sampling error can be reduced by
The margin of error is reduced.
There can be no set value. An acceptable level of sampling error for a company making high precision machine parts is likely to be very different from the sampling error for household incomes, for example.