Musashi's, and Miyazaki's, concern is the volume of anime that seems aimed at a least-common-denominator audience.
What I don't like is bad anime, and there is a lot of it.
Maybe my perceptions are biased by what is available here in the States. If so, then we seem to be a dumping ground for an awful lot of bad television and film, most of it aimed towards socially inept teenage boys. Throwing it on a bronze disc with Dolby 5.1 surround sound and english subs doesn't make it better, just more accessible. You know that character who runs the local comic shop on The Simpsons? Now, you and I know that not all anime fans are like that guy...a socially maladjusted recluse. But judging by what's on store shelves, it wouldn't be surprising. Simplistic or infantile plots, usually revolving around suggestive liaisons between alien pre-teens and awkward male human boys, are more often than not standard anime fare.
I don't see things as being quite that bad...there's a lot of good stuff out there as well (Best Buy carries stuff like Cowboy Bebop and Ah! My Goddess). And while I don't think Sailor Moon is right up there with Record of Lodoss War, one of the reasons for its popularity was its appeal to girls. I think Musashi and I share a perspective from our own experiences...when we were growing up, anime was fairly rare, and you took what your local independent TV station could get on the cheap. As a result, I grew up with bad anime (Speed Racer), but it gave me a taste for the genre, which only grew as I noted the higher quality of almost everything else. I myself am using Sailor Moon to introduce my daughters to anime.