Does it really need to correct the error?
Not necessarily. As you go on to say ....
A simple, short checksum, typed in by the person answering the phone, along with the W3W, would immediately identify there was an error in the three words, or the checksum, so they ask for a repeat.
That would usually be fine, provided that there were adequate communication and time for a repeat to be requested and provided. That will nearly always be the case, but is not inevitably the case in some 'emergency situations. However, doing a bit of 'thinking aloud' ...
1... The above would work, but would obviously only serve to indicate whether or not the 'intended' three words had been communicated correctly, but clearly could not detect the correcr communication of incorrect words (e.g. ones which were not used by W3W).
2... if there is a single-character error in communication of the three words then, as you suggested previously, an error could be detected by addition of a 4-digit numerical checksum. If one assigned a numerical value (0-25) to the letters of the alphabet, and simply added up the values for all characters of the words to get a checksum, a 4-digit numerical checksum would be adequate for up to 384 characters in the three words. In fact, a 32-digit numerical checksum would be adequate for up to 38 characters in the three words, which should be enough. The same would also nearly always work if there were two or more errors in the words, but (as with any checksum situation) there would then be a finite probability that the coded values for the erroneous characters would 'cancel', leading to a seemingly correct checksum despite the errors.
3... a lot depends upon where the W3W has 'come from'. If it is automatically generated and displayed at the time (e.g. on the screen of a phone, tablet or watch), then the above (with the checksum) ought to work satisfactorily - detecting a transmission/communication error (in either words or checksum) in what was communicated.
However, if the W3W (and checksum) has come from a person's memory, or from a record of it they have made themselves (on paper, in a device or whatever), then it is possible that what is remembered or had been recorded is incorrect, in which any number of 'repeat transmissions' will result in the same erroneous information (with a checksum error) being repeatedly transmitted.
4... in terms of 'remembered' W3Ws, I've already observed that adding a numerical element, even if only 4 digits, would do a lot to undermine the concept of W3W
5... thinking aloud even more, a fair proportion of the sort of 'incorrectly communicated' W3W words that have been mentioned could have been avoided by careful exclusion of some types of words from the W3W system, such as the avoidance of:
plurals
words commonly mis-spelled - e.g. if their correct spelling differed from intuitive/phonetic'expectations'
words with 'alternative' spellings and/or pronunciations
words with internationally-differing spellings
etc. etc.
Just a few thoughts!