If the wrong date of the accident is on my summons and does not match the date on the citation I received, could this result in my case being dropped?

You know, it depends.  If you have a competent lawyer, it's a fact to utilize at trial if it fits your theory of the case (like sloppiness or poor police investigation).  It could be a complete clerical error or it could be actual confusion. A skilled trial lawyer may be able build multiple erroneous dates into his or her theory of the case. It's not likely to, independently, dispose of the case. It's another fact that could potentially be used at trial. 

Most likely the discrepancy of dates on your summons and the citation will not result in the legal action against you being dismissed. The discrepancy is most likely the result of some clerical error.

You should be prepared to show up in court to defend yourself with necessary paperwork, photographs and witnesses if the offense is a traffic violation. If the offense is a traffci violation and the citing police officer fails to appear, then the action against you will most likely be dismissed.

If the court proceeding is more serious, such as a misdemeanor or felony criminal charge, you should seriously consider retaining a qualified criminal defense attorney to protect your interests.

A criminal action could result in jail time or a substantial fine.

Good luck.