Recently found out that the last complex I lived in reported me to Resident Data as "evicted", even though I turned in the appropriate notice, was not behind on the rent, and received my full security deposit. I moved a year ago from this complex, and have received no notification or any communications from them in that year. However, when I called them today, they told me I'd had late fees on my account, but because it's been a year, they did a "charge off" of the late fees and there is no way to correct the "evicted" status on my report.

I'm still researching, but wouldn't a notice of eviction have to go through the local court, and wouldn't they need to give me notice of it? I had no idea that this had occurred, or I would have contacted them sooner to resolve the issue. I was never made aware of late fees outstanding, I wasn't contacted to recoup the fees either by the complex (locally owned and operated) and I wasn't contacted by a collection agency or court agent. If I'd not applied for a different apartment complex, I might have never discovered this on my record.

What are my rights in getting the status changed on my record? And how long does the status stay that way? I recently married, and even though my spouse's record is clear, we've been rejected for another complex due to this. Does this mean we can never move?

Yes, a official eviction has to go though courts.

I would notify them by certified mail that this is to be corrected.
Then challenge this on the credit report, it would be taken off if they don't come back and confirm it after you challenge it.