The Super Buddies
The past is like wet cement. 
The DC Universe is a stupidly complicated place. In an ideal world, all of the continuity would make perfect sense and everything would fit together perfectly. However, in a shared universe containing thousands of characters built by hundreds of creators over the course of several decades, this is just too much to ask for. Sometimes it's an editorial edict, sometimes the writer just messed up. So rather than staying up crying into our cereal attempting to decipher this hot, wet mess, we have created this handy guide. If you are ever presented with a retcon that just absolutely doesn't make sense, even in the constant reality-warping Multiverse-changing context of the DCU, feel free to shrug and pick a random item off this list.
If your issue was published pre-2011
Retroactive continuity waves
The end of events like Crisis on Infinite Earths, Zero Hour, Infinite Crisis, etcetera, changed the timeline various times. If a change is not immediately present, retroactive continuity waves will soon realign or diverge over the aspects of an event.
Hypertime
Mark Waid created this really cool concept called Hypertime, specifically for people like you. The idea is that time is like a river with tributaries constantly flowing in and out, so time is changing all the time and nobody even realizes it. That's why Black Canary had the wrong eye colour in that one issue of Justice League you thought might be valuable. Hypertime.
Superboy-Prime punching reality
Superboy-Prime punched the walls of reality themselves, irreversibly changing... whatever writers wanted him to, basically. This is an intentional catch-all excuse for anything that goes wrong, so they covered themselves pretty well.
The Decreator
Grant Morrison introduced this really cool idea in his Doom Patrol run called the Decreator, a malevolent entity created when God cast a shadow at the beginning of time. He is slowly in the process of erasing the entire universe, although it's been slowed down to a rate where it's barely noticeable. Maybe he "ate" whatever editorial mistake you're complaining about.
Something something something Zero Hour
I'm going to be completely honest here and say that nobody actually read Zero Hour. It's probably responsible for changing whatever that thing is. Because, you know... entropy... and stuff.
Dan DiDio
If all else fails, and you absolutely cannot find an excuse that satisfies your nerdy problem, it's easiest to just blame Dan DiDio. Try screaming his name while you shake your fist angrily at the sky in a thunderstorm. Remember, he was the only person working at DC who ever did anything wrong.
If your issue was published post-2011
In 2011, DC Comics rebooted its entire universe, seemingly to make all our lives more difficult. But, despite what you might think, it's really tough to start a whole universe from scratch and things fell through the cracks. Now we have a new batch of excuses... er, I mean reasons - why facts between issues are inconsistent.
Flashpoint
The canonical reason the entire universe was rebooted. A superhero went back in time for, like, the millionth time but this time, the Flash broke everything and Pandora pieced it back together. In reality, an inconsistency is probably because all the creative teams were all over the place with what was canon or not in this new rebooted universe, but, if it makes you feel any better, you can say it's because all the pieces of the timeline didn't fit quite right.
Milk Wars
The characters from DC's Young Animal imprint teamed up with some of the mainline heroes to stop a higher-dimensional corporation from selling their reality to a higher-dimensional big wig. It was wild. But the corporate-meddling resulted in an updated version of our current reality where maybe your retcon was one of the changes. Robotman became human again for Pete's sake. And then they made him a robot again in the next issue he appeared. I'm still mad about it.
Superman Reborn
If it's a Superman thing, Mxy did it. The time-duplicate New Earth version from Convergence and the Prime Earth version were merged by that order-hating freak, Mister Mxyzptlk. We say merge, but it was pretty much a take-over, as the Prime Earth Lois & Clark were unceremoniously killed off just before. It's almost as if they did Convergence just to get rid of the new Superman. It's nice and vague, so if the story even remotely involves a Superman character, blame the imp.
Doctor Manhattan and Rebirth
When DC made an initiative to backtrack all the changes they made with Flashpoint, they called it DC Rebirth, you can read more about it. But, there we discovered that Watchmen's Doctor Manhattan came to the DC Universe and just poked things around in the timeline to see what would happen. Surprise! It retconned a lot of things. And even though he eventually tried to fix it, all of history's really flexible because of him. Any major inconsistencies post-Rebirth are probably because of this flimsy timeline.