I am getting the following error:

error (247) arithmetic overflow during implicit conversion of VARCHAR value '01/01/2010' to a DATETIME field.

when I execute the following proc with two date parameters:

EXEC somedb.dbo._p_proc '01/01/2010', '01/31/2010'

Parameters are: @start_date DATETIME, @end_date DATETIME.

I am not sure what the problem is?

Please paste the full code. Only that can help.

It looks like you values are not in correct format for datetime type.
Check this, it may help.

Entering datetime and smalldatetime data