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I'm sorry to hear about your situation. Technically the eviction doesn't show up on a credit report, but on a tenant screening report. It's done at the same time, as part of your background check. You want to find out first which company was the one that reported this. You also want to go to the court and get a copy of the docket and/or order of dismissal to show that it was dismissed.
Once you find out what tenant screening company is reporting this information, contact them, dispute the information and incorrect and incomplete. You should also tell your landlord that reported this information that he has an affirmative duty under the Fair Credit Reporting Act (FCRA) to notify them that this was made in error, that you were never delinquent and should not have gone to eviction in the first place.
If the landlord doesn't do this, you can bring a case against the landlord and the tenant screening company. If it gets to that point, you need to contact an attorney in your area that deals with tenants rights and credit repair cases. Go to www.lawyers.com or www.legalmatch.com to find an attorney in your area. You should be able to find one that will give you a free initial consultation and better advise you of your rights, any problems with your case, likelihood of success, how courts are treating cases such as yours in your area, and what you should do next.
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for the time and effort that I spent on this answer unless and until you rate it positively (3 or more stars). Thank you, ***** ***** luck to you!