Yes, that is mildew - a common problem for many begonias during the fall/winter months especially if they were outdoors and then moved indoors. Spray with fungicide to reduce/prevent further outbreaks; remove worst leaves; keep warm; etc, etc.

Mallets are some of the worst hit and often can be killed if not treated promptly, rexes and polka dot canes are a close second but usually can survive a full fledged outbreak. On canes do pay attention to the stems as well as the leaves since mildew will often go unnoticed there. Lucerna can be severely attacked on the cane itself for example.

A product called Milstop has pretty good results against mildew but is hard to find other than on-line. It is costly as well but you get a five pound bucket of the stuff for around $70 (shipping included - at least it was last year). A tablespoon per gallon of water goes a long, long way.

Hcmcdole, thanks for your reply...this is that 'Midnight Magic' which you said often gets mildew. None of my other begonias have gotten that so far. I hope it's not fatal! It looks good otherwise, even has 3 big blooms coming up.

That is minor damage and won't do any signifciant damage. You can cut the leaf off if it gets too unsightly. Do keep an eye for spreading spots. When the entire leaf or stem gets white then you know you have serious problems. I lost Lynda Dawn (a very dark leaf Mallet) in late summer/early fall from mildew. I could not believe how fast it went downhill to ultimate death. I could understand if it did it in very cool weather but it was still very warm in September.

hcmcdole - you lost 'Lynda Dawn'? Aw that is my hybrid, created it in the 90's. If the weather was warm it is not mildew. Mildew ONLY thrives under cool, moist conditions. More than likely it was just fungus from moisture. I have a pic of 'Lynda Dawn' on my blog at planetbegonia.blogspot.com.
And yes, greybird, it is mildew. Increase air circulation to your growing area to prevent mildew.

How about brown spots on upper leaf surface of "Castaway" with the under surface (which is deep red) of the spots are light green? Thanks.

I stopped mildew on Lucerna's stem using hair spray to coat it. I don't recall whose suggestion it was originally but it did stop the mildew, changed the color of the green stem but that was not important to me.