wrote
each broken bolt went through a threaded hole in
the water pump base into another threaded hole in the lower unit. Seem
like the threaded holes in the water pump base had some chemical
reaction with the bolts, and the threads in the hole in the water pump
base had completely corroded away

Take a look at a new water pump base for reference. I'll bet there aren't
supposed to be threads in the holes. (Doesn't make sense mechanically to run
a bolt through one threaded hole and into another.)

I ended up messing up the thread in one of the
hole in the lower unit (the other three are fine). I don't know what
is the best way to deal with this. I will bring the lower unit to a
marine mechanic in this afternoon to see if he can help.

The standard way to fix something like that is with a heli-coil insert.
http://www.emhart.com/products/helicoil.asp