These are the problems I have seen (and survived through - those who
are interested may come study my scars):
1. Asking for advice after getting into a situation.
It has always seemed to me better to read a lot about some new choice for one's life "before" getting into it. This is where I saved myself a lot of grief. Silver Moon and I read a lot over several years, in fact, before we even attempted to have an actual poly relationship.
2. Failing to see that experience will always be different from whatever it may be that you think it will be.
I am still amazed that people who are intellectually okay with their partner dating another are surprised by the emotional issues that come up when it actually happens. Emotional issues must be worked on emotionally, not intellectually.
3. Expecting others to be honest about something they don't really understand.
You can't be honest if you don't know what you're doing. The most you can be honest about is your ignorance. Many polys get involved with someone who has never had a poly experience, but who says they'd be okay with it. Then the real poly discovers the new lover is a cowboy and a "secret" monogamist.
4. Considering your new lover as of equal importance to your long-term love (especially if you live together with the long-term lover(s))
People are constantly destroying "all" their current loving relationships because they don't give the old love priority in a conflict (assuming both parties are equally comfortable with poly). It goes this way: They fall madly in love with the new relationship (who, all too frequently, is not really poly). Then, when some problems come up in their primary or long-term relationship because of the new love, they choose the new love over their long-term love.
The rule is really useful. Work on the problems with your long-term lover (or: primary) and hold that to be of "more" importance than the hot new lover.
5. Keeping their feelings from their lovers.
Despite the mantras about talking, the advice to be open and honest, many polys are afraid of the consequences of letting their loves know what they are feeling. Once the secret resentments, worries or attractions have festered for a while, they rot the existing relationship. It is not just a good idea to be open, honest and keep talking, it is essential to a healthy polyamorous relationship (or even a healthy monogamous one). Poly relationships will fail faster over such issues than monogamous ones.
6. Failure to give each partner quality time.
I know "quality time" is a pop term, but it refers to giving a lover your full attention with no distractions for a time. Each lover needs some of that time every few days or more often (of course, this varies with the personalities). What often seems to happen is that we give the new lover all our quality time, while spending busy-work time with our old relationships. We short-change the lover we feel confident of, thus damaging that relationship, in favor of the hot, but not yet settled realtionship.
7. Avoiding "hot" topics.
It's truly a wonderful and strange thing to notice that people will often assume what another person would think about something that's never been discussed. This is like the teenager who's embarrased to find her parents are having sex because she assumes her friends will disapprove if they knew (and somehow seems to think they will know without ever being told). By keeping something important to your own emotional health to yourself, you begin to resent your partner for not approving of you and you're acting out of total ignorance.
Most of these things I have either done or seen done (and avoided like a plague when I saw the results). If you look at them carefully, they all refer to any loving relationship, monogamous or polyamorous. Folks who think poly is harder are just commenting on a simple fact: It's much easier to hide myself from one person (monogamy) than it is from more than one (polyamory).
Just because you can hold a monogamous relationship together easier when the relationship itself has been destroyed, does not mean monogamy is actually easier than polyamory. I lived in a destroyed relationship for 15 years out of a 25 year marriage. I doubt I could keep a polyamorous marriage together 15 months under the same circumstances. Many of my friends have had the same miserable experience with monogamy.
Isn't it better to end the pretense of success when faced with real failure soon rather than late? I wish I had. So do my friends.
Problems with polyamory? Of course. They're called "skills of intimate relationships." At least in my opinion.