When is the best time to "break-apart" a cluster of hostas? I have
two large clusters of them, and would like to thin them down some and
spread them out.

I did it in the spring (not long after the leaves came up). They
seemed to take it pretty well (they didn't droop as much as other
plants like black eyed susans do when I divide/move them).

According to http://perfectperennials.tripod.com/id8.html you can
divide hostas any time of the year, though.

Also, have a rose bush that has had the dreaded "black spot" for
years now.

Well, I'm sure it is heresy but our roses have it (or something which
looks fairly similar), and we just ignored it. The diseased leaves
fall off (either in the autumn, or early), and the new growth doesn't
really have it bad until it has been there a while. We've only been
through one season of the "ignore it" strategy, though.

Antique roses are said to be less susceptible, and keeping air
circulation around the plant is said to help.