It's true that the selection of adjectives isn't the best but I do think that it is a decent set, considering that I think the set has to be somewhat restricted so that an overlap of differing people can grow out of the responses. Possibly it might be better if each person got to choose some 60 adjectives out of a much larger set that included some negative ones. But there might be something to be said for everyone having the same set. I know that I got to determine a lot more about what I meant by the various adjectives by choosing them for many different people.
I think it's also good that you can only choose a few — 5 or 6. Needing to choose whatever comes to mind first or whatever you think is most striking or most important about someone. I know that there were quite a few where I wanted to choose more but I had to restrict my choices. I'm glad that the order that the adjectives were chosen was kept since that was usually but not always another datapoint with me. I think that pulling the data on which adjectives I chose for the various people and how often would be cool but I don't think there's really a way to do that easily.
It's also not designed to be psychologically insightful. Looking at the wikipedia article and a few others out there, the Johari Window is designed for exploring relationships and as an icebreaker at social events where people are acquaintances rather than friends. Nothing really deep here or even peer reviewed.
Finally, it's a bit of fun. Some people enjoy participating in these things and some people don't. It can be annoying when lemes like this take over one's friends page but it's just something that comes with the territory.