Two problems related to automatic transmission have been reported for the 2005 Honda Civic Hybrid. The most recently reported issues are listed below.
Honda recall for judder in cvt on 2005 hybrid. Repaired (I believe by burnishing the clutch?); however, condition is recurring, gradually getting worse. I have heard many other complaints of the same problem in other cvts. My sons recently had the same repair done to his.
Cruise control drops out unexpectedly when traveling at highway speed.