A month ago I went into my apartment complexes office and handed a typed 60 day notice to the person at the front desk. They lost the notice or misplaced it. When the my new landlord called my current landlord for a reference, I got a rather unhappy surprise when my new landlord was told I hadn't given notice. Now I did take a digital photo of the dated notice with my phone prior to giving it to the person at the desk of my apartment complex. The photo which is dated, has location data on it showing I took a photo in the apartments business center which is in the room next to the office. If they don't let me out of my agreement are there better avenues than court for what they have to do? Are there requirements that they have to prove they received the notice? Do they have to honor the notice or can they just continue to say we didn't get it. As this would seem unfair to tenants.
There is no law requiring a person to say nice things about you, or specifically for a landlord to give a positive recommendation. However, you can sue a person for defamation, if they have said untrue things that harmed you. You would then need to show that he said things, that they were untrue, and that you were harmed. The main issue on the first point would what exactly he said. A subjective stars rating is neither true nor false, nor is a comment "I would give negative 5 stars if it were possible". The statement "Smith abandoned his apartment without giving the required 60 day notice, thus breaching his lease" could be true or false. You would then need to provide believable evidence that the statement is false. You would need to hire an attorney versed in local defamation law and practices to know whether your evidence would be deemed sufficiently credible, but on the face of it, you have fairly good evidence (assuming that they don't have iron-clad proof that you never entered the office). Then you would have to prove that you were harmed, requiring some legal remedy. One out-there option would be to sue them for a million dollars: it is unlikely that you actually suffered a million dollars damage. On the minimal side, you reputation has been besmirched, and a letter retracting the accusation would certainly be appropriate. Your attorney would advise you of the best remedy.
It is not always necessary to file a lawsuit and pursue the matter through the courts. One might get a satisfactory result by having an attorney write a letter outlining the wrong that the other party has committed, and what you want by way of remedy. Even before that, you can (for free) inform them of what actually happened and mention that you'd prefer not to have the courts resolve the matter.
It is not clear whether you mean that the former landlord is suing you for breach. If so, your concern would be showing that you complied with the terms of the lease, especially that you did deliver the notice to the correct location in the correct manner in a timely fashion. Leases do not typically include onerous notice requirements (whereas legal notices may require delivery by certified mail). Again, the main factual question would be whether you did comply (and thus did not break the leash).