The eagles! The eagles! They're the most obvious example...heck the whole story
is based on Bilbo's "chance" finding of a golden ring in a dark cave!
I assume we will talk more about the eagles at an appropriate point in the
future...while their continual appearance in the nick of time seemed a bit much
too me, overall i don't see it as laziness, but rather fitting into Tolkien's
cosmic order and morality...good things, albeit unexpected, come to those who
show courage and determination to do the right thing.
Mercy, or pity, obviously plays a huge role in this story. Bilbo and
later Frodo's treatment of Gollum topping a long list of examples. Here
the Rohirrim show mercy to the Dunlendings, showing a) while not "civilized" in
the modern sense they do have some moral values, b) perhaps atoning for some of
the sins they comitted against the "backward" Dunlendings in the past when the
routed them out of their lands.
The simple explanation for why no mercy to the Orcs is that they all died or
disappeared in the forest. And in general Orcs expect no quarter and give
none in
return.