The smaller the standard error, the less the spread and the more likely it is that any sample mean is close to the population mean. A small standard error is thus a Good Thing.

What standard error is acceptable?

A value of 0.8-0.9 is seen by providers and regulators alike as an adequate demonstration of acceptable reliability for any assessment.

What does a high standard error mean?

The standard error tells you how accurate the mean of any given sample from that population is likely to be compared to the true population mean. When the standard error increases, i.e. the means are more spread out, it becomes more likely that any given mean is an inaccurate representation of the true population mean.