A lot of these problems, as she admits, are actually problems with the social machinery of enforced monogamy. "Rejection by family, friends, etc.," not knowing which partner to take to a party, and the inability to run for political office aren't problems with polyamory; they're problems with prejudice against polyamory.
About the claim of "increased drama:" I don't know that drama is increased in a poly relationship, and I would claim that it isn't. I know of and have (alas) been in mono relationships characterized by constant drama, usually as a result of someone's deep insecurities. Monogamous relationships set themselves against the natural human tendency to wander and explore, and monogamists know it, and the result is often a lot of suspicion and paranoia, and snooping in people's cell phones and email boxes and condom packages. Snooping is HUGELY dramatic in a lot of monogamous relationships, and is usually less of an issue in poly. In my experience, a poly relationship in harmony with that basic human nature to explore new territory and find variety is far less dramatic.
About the challenges with time management: well.... "duh." But I think that is true of any relationship. Monogamous couples also must manage their time between their relationship and their career, friends, hobbies, etc. I also tend to think that time management is more a problem for smaller poly families (triads, quads) and vees/stars than for tribes. It's easy for a member of a triad or quad to feel left out of activities, but there's always someone around to be with in a tribe.
Poly relationships are different, but honestly, I can't think of a single real down side that doesn't have to do with social condemnation. If you can rise above that, I don't think there are any problems directly related to polyamory itself, which is in closer harmony to the actual, real, non-fairytale human condition than strict monogamy.