In general, you should use a distance large enough to ensure that every feature has at least one neighbor. An asterisk indicates a distance that does not ensure that all features will have at least one neighbor. Some tools such as Cluster and Outlier Analysis and Spatial Autocorrelation require each feature to have at least one neighbor.
If a smaller distance is more appropriate (if it better matches the scale of the question you are asking), you can create an .swm file using the Generate Spatial Weights Matrix tool and set the Number of Neighbors parameter to the minimum number of neighbors each feature must have. If, for example, you set the minimum to two, the search distance for any feature with less than two neighbors will be expanded for only that feature to capture its two nearest neighbors.