Who would know how to manage rainwater erosion on a sloped property?
Erosion:


Establishing a deep rooted vegetation may help.  What would work best
is dependent on where you live.  Your local conservation office would
be able to help with what would work best in your area.  This
site has some good information for choosing plants on slopes.
Rip-rap (rock) is also commonly used to help slow erosion.  The size
you would need would depend on the slope and flow of a the drainage,
if it would be within a drainage area.



Source: http://www.erosioncontrolnetwork.com/rip-rap/rip-rap.aspx
Another option would be gabion baskets, however they would be one of
the most expensive options.  Gabion baskets often look like chain
link fencing wrapped around rock.  In this way the rocks stay in
place and the can be placed in a more vertical position.



Source: http://www.svca.on.ca/page.php?page=erosionandfloodcontrol


Flash Flooding:

The first thing I would do is establish who is responsible for maintenance of the ditch.  The capacity may need to be re-established or increased if run-off from additional developments have been added to it.  If increasing the capacity of the ditch is not an option, I would see if I could construct either berms (a slight rise in topography) or swales (a minor trough in topography) to direct the water away from any structures on my property.  However, you would need to make sure that you are not increasing flow onto any other neighboring properties or impeding flow from any other properties.

Ponding:


Dry wells are often used to address ponding in yards.  They are
basically an underground chamber that water is directly to through
pipes.  Holes in the container let water slowly soak back into the
surrounding soils.  These need to be sized properly to accommodate
the volume of water one is trying to remove from the surface of their
yard.  Also, these may not work well in clay soils that the water
would percolate slowly into.  More information can be found at the
source link below.



Source: http://www.svca.on.ca/page.php?page=erosionandfloodcontrol
Rain gardens are a more decorative option that includes water storage
in a depression, water infiltration,and native vegetation. The basic
idea of a rain garden is captured in the image below.  Additional
helpful information can be found here.  Some municipalities may
also have funds available for installing rain gardens on private
property.

 

Source:
http://vienna-wv.com/portal/2013/07/18/what-is-a-a-rain-garden/


Again, I would definitely contact the local jurisdictional authority before I do anything.  There are many government agencies that have codes that need to be met.  Additionally, they would know what works best in your area and may have subsidies that would help defray costs.