It looks like you have the index field for the update set to the ClinicCode column. For the value you are using Request.Form("WADAUpdateRecordID"). This form element is set to WADAdboHICOMClinicsAndDoctors.Fields.Item("ClinicCode").Value which should be the ClinicCode that comes from the recordset. You are filtering the recordset on this value being either -1 or Request.QueryString("ClinicCode") if it is present.
So long as you get to this page and filter the recordset on this value, and this value is unique in the db it should only update this individual record. The only way that I can see it updating more than one record would be if more than one record had the same ClinicCode before you got to this update page.
The best way to avoid this type of thing with the update it to reference the unique primary key for the table, this would ensure that the value was unique and that only a single record would be updated. I would suggest that you set this field to be the primary key if it is to be unique for each record, or add an index that is a primary key that will be unique for each record. If you add an index you will want to update your recordset on this page to get the id and then update the update server behavior to set this id column as the index field for the update.
If you can post back with an export of the db with just this table in it in a MS Access file I can take a look and do some further testing for you.