What is the correct way to ensure unique entries in a temporal database design?
The safest way to do this is to enforce your business rules using the built-in referential integrity constraints, as Alexander Kuznetsov describes in his article, "Storing intervals of time with no overlaps".

Applying the techniques listed there to your sample table results in the following script:

CREATE TABLE [Z_STORE_TEAM](
    [STORENUM] [int] NOT NULL,
    [TEAM] [varchar](10) NULL,
    [EFFECTIVE] [date] NOT NULL,
    [FINISHED] [date] NULL,
    PRIMARY KEY CLUSTERED 
    (
        [STORENUM] ASC,
        [EFFECTIVE] ASC
    )
) ON [PRIMARY];

INSERT [Z_STORE_TEAM] 
    ([STORENUM], [TEAM], [EFFECTIVE], [FINISHED]) 
VALUES 
    (1, N'1', CAST(0x01380B00 AS Date), CAST(0x81380B00 AS Date)),
    (1, N'2', CAST(0x81380B00 AS Date), NULL),
    (2, N'1', CAST(0x01380B00 AS Date), NULL);


Modifications:

-- New column to hold the previous finish date
ALTER TABLE dbo.Z_STORE_TEAM 
ADD PreviousFinished date NULL;
GO
-- Populate the previous finish date
UPDATE This
SET PreviousFinished = Previous.FINISHED
FROM dbo.Z_STORE_TEAM AS This
CROSS APPLY
(
    SELECT TOP (1) 
        Previous.FINISHED
    FROM dbo.Z_STORE_TEAM AS Previous
    WHERE 
        Previous.STORENUM = This.STORENUM
        AND Previous.FINISHED &lt;= This.EFFECTIVE
    ORDER BY 
        Previous.FINISHED DESC
) AS Previous;
GO
ALTER TABLE dbo.Z_STORE_TEAM 
ADD CONSTRAINT UQ_STORENUM_PreviousFinished
UNIQUE (STORENUM, PreviousFinished);
GO
ALTER TABLE dbo.Z_STORE_TEAM
ADD CONSTRAINT CK_PreviousFinished_NotAfter_Effective
CHECK (PreviousFinished = EFFECTIVE);
GO
ALTER TABLE dbo.Z_STORE_TEAM
ADD CONSTRAINT UQ_STORENUM_FINISHED
UNIQUE (STORENUM, FINISHED);
GO
ALTER TABLE dbo.Z_STORE_TEAM
ADD CONSTRAINT FK_STORENUM_PreviousFinished
FOREIGN KEY (STORENUM, PreviousFinished)
REFERENCES dbo.Z_STORE_TEAM (STORENUM, FINISHED);
GO
ALTER TABLE dbo.Z_STORE_TEAM
ADD CONSTRAINT CK_EFFECTIVE_Before_FINISHED
CHECK (EFFECTIVE &lt; FINISHED);


An attempt to insert the fourth row of sample data now fails with an error message:

INSERT [Z_STORE_TEAM] 
    ([STORENUM], [TEAM], [EFFECTIVE], [FINISHED]) 
VALUES 
    (2, N'2', '20140201', NULL);




Please read Alex's article to understand how these constraints ensure your table data will always be valid. Having a set of constraints enforce your data integrity means no trigger code is required.

Related article by the same author:

Modifying Contiguous Time Periods in a History Table