i'd say it's a bad trigger.

it does not handle multiple rows at all.

there may be a logic hole here as well: it updates the entire contact2 table for any row with the same account number.

a trigger should be updating based on a join from the inserted table.

I'd think it needs to look like tis:

CREATE TRIGGER [Db_Officer_Filler]

ON dbo.CONTACT1

FOR UPDATE, INSERT

AS

UPDATE MyTarget

SET MyTarget.uacnt = users.name

FROM contact2

INNER JOIN INSERTED

ON MyTarget.accountno = INSERTED.Accountno

INNER JOIN users

ON users.name = inserted.u_key3

WHERE ISNULL(inserted.u_key3,'') <> ''