I definitely think it is worth monitoring and recording them, but I'd be cautious about exactly how that was done - given the very variable quality of such things, I'd be a bit wary about putting such data straight into the main complaints system and risking skewing "real" complaints data.
My approach would be to log each one, use the relevant platform to make contact with the complainant, and determine actions from there - if you can get legitimate detail to substantiate the complaint (traceability information, proper detail about the issue etc) then I'd transfer into your normal complaints system. In the absence of such information I'd just keep it in a separate record of unfounded/questionable "noise". You can still do some trend analysis etc on it to look for potential real issues, but equally if it's just anonymous postings on review sites etc I'd still be sceptical unless it's something that you can verify from other sources and/or your own testing.