The reason betadine is not a good purifier is that the iodine is not immediately available in the solution.
But in a nutshell, it is used for hand purification, surgical preparation, etc, because of its sustained release properties....good if you are going to need sterile hands for an hour, bad if you want to achieve high immediate concentration.
I would love to use betadine, as it is cheap and readily available, but delayed release is not what you want.
see excerpt from zen backpacking...
"Providone-iodine is a polyvinyl pyrrolidone-iodine water soluble complex that works as sustained-release reservoir of free iodine. This enables providone-iodine solution to contain high levels of iodine without being too irritating to skin and without losing free iodine when mixed with water.
This disinfectant is often carried in first aid kits and because of its versatility as both a topical antiseptic and water purifier, it is the preferred chemical water treatment option by many backpackers, climbers and other outdoorsman. But since it contains both povidone-iodine and free iodine, you are consuming conceivably more iodine than if you used just iodine alone to treat your water.
The concentration of free iodine in providone-iodine solution is a complex matter. Dilution of providone-iodine in water seems to weaken its hold on iodine, causing a release of free iodine into solution. At full 10% strength, the concentration of free iodine is actually lower than when diluted down to 1:50 with water. This increase in free iodine concentration begins to decrease somewhere around 1:50 dilution but concentrations differ amongst the various brands and formulations and is difficult to calculate."