If your data in the original dataset you importing FROM has errors, it cannot import correctly.  Open the contacts lists (individuals, couples, others, groups) and make sure none of the names are blank and that you don’t have any dashes, “unacceptable characters” such as rectangles in the fields.  *CAUTION – If you get an error part way through your contact list and import it again after you have made corrections, you will duplicate all contacts that were successfully transferred before.