Why do you think forecasts can go wrong?
- not perfect initial condition (cannot measure the atmospehic variables everywhere perfectly)
- not perfect mathematical model (description of the large scale dynamics can be perfect, but other physical processes (like cloud physics, radiation, PBL, surface, non-hydrostatic processes) have to be simplified or indirectly included those overall effect - parametrization)
- because of limited computer resources equations cannot be integrated perfectly. Resolution (time and space) is limited so the unresolved processes have to be included in some indirect way (parametrization).
- and on the top of these the chaotic behavior of the atm. dynamics (even if a very simplified version) can lead fast growing error from the almost perfect initial condition

How does ensemble forecasting address (or does not address) the reasons for 'providing wrong forecasts' you have outlined above?
With perturbed initial condition, perturbed model (stochastic physics) we can get many more or less equally probable forecast scenarios instead of one single forecast with no information about uncertainties.

What is the EDA?
Ensemble data assimilation :)

What constitutes a 'good' ensemble forecast?
- more or less equally likely scenarios 
- flow dependent spread
- ... we can list many other features in connection with different verification measures

What is the set up of the ECMWF Ensemble forecasting system?
50 perturbed forecast + 1 control forecast (with the same analysis and physics with HRES) 32km/91levels, 64km after 10 days

Questions:
As far as I understand we have 25 members with EDA and 25 members with perturbation based on singular vectors. Can we know which member belongs to EDA and singular vectors, based on the numbering of the members? Could it be any practical benefit for operational forecasters to know more information about uniq features of different perturbed EPS members or we can use them completely equally in every situation?