I haven't used it in several years, but looking back at my 400H old pictures I notice two things:
1. The shadows drop out abruptly with careless exposure or under difficult (high-contrast) conditions. This might have more to do with the processing and scanning than with the film (I was using a commercial service, since I don't do my own C41 processing), but it tends to support the point Rolfe Tessem made: meter carefully or allow 1/3-2/3 stop extra exposure as a safety margin.
2. I don't like what 400H does to greens. It renders purples and yellows beautifully. This is a matter of taste, and it's not surprising given 400H's original market as a (wedding) portrait film, but it's worth bearing in mind when matching film to subject.