Currently Jira assumes that all date fields are date picker fields. The problem is that generally the date-time format is different to the date format, but the csv import does not take this into account and so the following error is thrown.

[16:52:26] FAILED: Customfield value 13-Feb-04 is invalid
[16:52:26] com.atlassian.jira.issue.customfields.impl.FieldValidationException: Invalid date / time format. Expected dd-MMM-yy hh:mm a
at com.atlassian.jira.issue.customfields.converters.DateTimePickerConverter.getTimestamp(DateTimePickerConverter.java:50)
at com.atlassian.jira.issue.customfields.impl.DateTimeCFType.getSingularObjectFromString(DateTimeCFType.java:50)
at com.atlassian.jira.imports.importer.impl.DefaultJiraDataImporter.importIssues(DefaultJiraDataImporter.java:478)
at com.atlassian.jira.imports.importer.impl.DefaultJiraDataImporter.doImport(DefaultJiraDataImporter.java:86)
at com.atlassian.jira.imports.importer.impl.ImporterThread.run(ImporterThread.java:21)

Jira needs to add the time information to the date field string.