Most irony goes unnoticed. Many people don’t really know what irony is.
I think troublemakers could use this fact to spread confusion by prefixing normal statements with, "I don’t mean to be ironic when I say this." Because irony is often non-apparent, people would spend a lot of energy and thought trying to find irony in places that it didn’t exist (or at least wasn’t intended).
I think it could also work, only slightly less well, with the classic, "no pun intended." Of course, in my case, troublemakers would say this only when there actually was no pun — intended or otherwise.