No symbol after the date indicates that the assigned date is certain. This is typically based on the inclusion of the date in the text of the document

^† indicates that although there is no date on the document itself, internal references or other evidence make the dating probable

^‡ indicates that there is no original date present in the record itself, and there is a lack of sufficient circumstantial evidence, so the date given is the best approximation
[?] after the date indicates that a date cannot be established with any level of confidence, and a speculative date or month has been assigned

See pp. 98-99 of Records of the Salem Witch-Hunt for more information about how dates were assigned.

Jan. 12, 1693^†