The permanent closure of my local ice cream parlor caused me to wreck havoc on the city.
The permanent closure of my local ice cream parlor caused me to reek havoc on the city.
The permanent closure of my local ice cream parlor caused me to wreak havoc on the city.
One letter can make a world of difference. Take our first problem sentence above. If we want to be technical, what that sentence actually conveys is something like the following: In my town, there was a local ice cream parlor that was closed. Its closure made me so upset, that I located havoc—the entity, here apparently anthropomorphized—and I beat the living tar out of it. Furthermore, I did this while standing on top of the city. (Oh, though if we wanted to change the text style and capitalization, what I could be wrecking is the new hit TV show Havoc on the City!)
If we then take a look at problem sentence number two, we’re in for even more fun. In this scenario, the ice cream parlor’s closure made me so upset that I decided to utilize my mighty stink glands to stink up havoc (again, the allegorical entity), and I did so while standing on top of the city. (I should note, though, that even this interpretation is problematic, as it would force us to accept a new variant of “reek”: a transitive verb meaning “to cause to reek”.)
The specific errors here differ, but the source is the same. Both “wreck” and “reek” are common words. “Wreak”, on the other hand, is far, far from common. In fact, I’m pretty sure the word “wreak” only occurs in the phrase “wreak havoc” (this expression, by the way, is a fun one since “havoc” is pretty rare itself, unless you’re a fan of the X-Men [though even there, his name is properly spelled “Havok”]). As a result, if you’ve heard it for the first time, or have never seen it in print, it seems reasonable to infer that the word “wreak” is either actually “reek”, used in some odd way you haven’t encountered previously, or that you misheard, and the word is actually “wreck”.
This latter interpretation is ingenious, in my opinion, because it plays on the context in which the word “wreak” is used. If a speaker uses the phrase “wreak havoc”, the context is probably negative (defined in the simplest way, to “wreak havoc” is to do something bad). Similarly, the verb “wreck”, defined simply, is to do something bad to something else. Since the semantic domain of both words is the same, and since the phonological forms are similar, it’s perfectly logical (or, perhaps, analogical) to assume that “wreak havoc” is actually “wreck havoc”, and that the meaning of “wreck” has been extended metaphorically to cover a situation that focuses on the act of wrecking something. The syntax of the verb, of course, has to be modified to allow for a direct object that itself isn’t “wrecked” (unless “wreak havoc” is interpreted as a phrase similar to “kick the bucket”), but given that words are used in such bizarre ways in English already, no English speaker can be blamed for making such an assumption.
Back to real world English, the status of this error, though, is that it is an error, and it’s not accepted even in non-standard writing. It will happen from time to time, of course, but just as we can’t get away with writing “for all intensive purposes”, so are we unable to get away with writing “wreck havoc”. As with other expressions, this is simply one to memorize, just as one must memorize that the word for “duck” is “duck” and not “cordoofle”.