One significant weakness in the official statistics in crime reporting is that there is likely to be unreported crime of all sorts in any jurisdiction. For example, rape is a significantly under-reported crime, as is spousal violence. Hate crimes are another category of crime that is under-reported. Thus the "official" statistics do not represent the real numbers or incidence of crime.
Another weakness is that definitions of various crime may vary, jurisdiction to jurisdiction. If all jurisdictions do not define a crime the same way, this becomes a comparison of apples and oranges.
One strength of crime statistics today is that the reporting of all jurisdictions should be easier than ever, with much reporting being done in electronic form. This should insure a greater accuracy, as well, to the degree that crimes are actually reported.