Your landlord apparently filed the eviction lawsuit in error and dismissed it prior to serving it upon you. Now the "residential screening report" is reporting the dismissed eviction action as a matter of public record. You are correct that complaining to the big three credit reporting agencies won't do you any good, given that you have told us that they don't list the debt. Further, credit reporting agencies are apt to respond that they are accurately reporting a dismissed lawsuit, and may do so as a matter of public record even if the lawsuit should not have been filed.

If you can narrow down the companies that produce the residential screening reports used by area landlords, you may be able to find a mechanism to deal with the situation or to have your former landlord attempt to annotate or correct the record. They may also be willing to give you a letter that you can submit with future rent applications, explaining that the error was theirs. I am not optimistic that they are going to be able to make a court record go away.