FireBrick said:

I planted a large rhododendron in my semi shade planter.
Heavy humus, a drip system to keep it slightly moist.

Make sure that "slightly" is the operative word, there. They're not desert
plants, and prefer a well-drained soil. They still like water, though.
"Slightly moist" is a good target, but often over-used.

Added appropriate rhododendron food once a week as per instructions.

Most of the gorgeous blooms are dropping now.

My question is, do you prune the stems of the petals, those little spikes
left after the petals fall?

Sure.


Or more correct question maybe:
What kind of care should I give now?

Prune it as you see fit, to the shape you desire, if it's done blooming.

As some of the woody branches are hanging slightly, can I control the shape
of the shrub by supporting those branches?

Or, if they're /that/ much "outta-whack", then prune them back. If there's
too thick of a cluster of limbs in the center of the plant, it's a good
time to thin those out, too. A good layer of mulch, up to but not against
the plant, would be in order.

HTH
--

Eggs

-A man walks into a bar with a slab of asphalt under his arm and says: "A
beer please, and one for the road."