Get your magnifying glass out and see if the dust is moving about, as it sounds as if you may have red spider mite. The black tips are the result of the damage that they do.
1; Cannas have large leaves, so mix some water up with a squish of fairy liquid in and wipe the leaves top and bottom with a sponge, rinsing regularly in the bowl of water. Then give it a good spray with fresh fairy/water mix. Now keep it regularly misted/sprayed. I had to use "Natures Answer" fungus and bug killer on my Erythrina in the end to beat them. Finally, allow the frost to get to it for a few nights, and hopefully it should come back next year bug free.

or

2: Dispose of the plant. Whatever you do, don't bring the plant indoors!!

Of course, if they're not moving around, the above tips are of no use to you.