This error usually comes when your query s returning more than one but u are capturing the result in a variable.Try to

change line in red,Either specify limit 1 clause or after querying the store them in the array .Look the red one.Change it to an arrar ,I mean list.

//Prevent deleting a contact that is associated with a 203k disbursement

trigger dontDelete on Contact (before delete)
{
  RecordType r =[Select id, name from RecordType where SobjectType='Contact' and name='Contractor' limit 1];
  for (Contact x : Trigger.old)
  {
    if (x.RecordTypeId==r.id)
    {
      x.addError('You cannot delete this an account of type "Contractor"');
    }
  }
}

Test:

@isTest
private class TestDontDelete
{
  static testMethod void myUnitTest()
  {

    Contact con = new Contact (LastName = 'Testi', RecordTypeID= [SELECT Id FROM RecordType WHERE Name = 'Contractor'].Id);

    try
    {
      delete con;
    }
  catch (dmlexception e)
  {
    system.assert(e.getMessage().contains('You cannot delete this an account of type "Contractor"'),
    e.getMessage());
  }
}
}

Ok need some answers...
1. Is the test class running perfectly in your developer org ?
2. Are you getting this error while deployment ?

If yes I guess , you need to check the target ORG.
The target org doesnt seem to have a REcordtype Named "Contractor" for contacts. Create one.