I think complaints are legitimate 100% of the time when the judge was obviously rude. If everything on the score sheet was perfectly accurate, but in overall it says "Quit brewing, your beer sucks!" then that judge should quit. *
Lack of completeness is a common complaint too, and legit if the judge didn't say anything, or very little. But sometimes its a checklist scoresheet because its a huge competition. One comment on each factor ought to suffice, along with some corrective suggestion on how to score better. I don't think its reasonable to expect a full brewing lesson.
In my opinion, entrants don't have a legit complaint if they just disagree with the judge's perceptions and scoring.
* I'd like to see a method for curtailing rudeness. If a competition gets a rudeness complaint it should be reviewed by the BJCP to determine if its legit, and then take appropriate corrective action, such as a warning followed by demotion or suspension followed be revoking credentials. A lot of people put in a lot of work just to have it destroyed by some ignorant or power hungry volunteer. Its rare I suppose, but it only takes one... rant over.