Steve.... there are several things that cause blooming problems. Most common are:
1. as Mike says, peonies need full sun... 4 to 6 hours a day. Your plant is right near the house, suggesting that light could become an issue.
2. it's a new plant. Peonies can take several years after planting or moving to start behaving.
The fact that you got one good bloom and several failed blooms makes me think neither is the problem here. It looks to me as if you have a condition known as bud blast. See the pic. Any stress can cause it. If you had a late frost or cold snap after the buds had begun forming (before you could even see them), it could cause bud blast. You might consider talking to the local extension service to see if perhaps lots of people are having bud blast this year.
That is a really pretty plant though, and I predict next year barring any late cold snaps, that you'll get good blooms.