You need to find the rows that don't convert. Try this out to find the offending rows:

CREATE TABLE #validdatesasints ( date INT PRIMARY KEY )

DECLARE @ValidDateStartValue DATE= '19000101' , --technically speaking you can go to the year 0001, but I wouldn't bother and it makes the lookup table v large

@ValidDateEndValue DATE= '21000101'

--same as above, can go to year 9999, but seems silly

DECLARE @Top INT= DATEDIFF(DAY, @ValidDateStartValue, @ValidDateEndValue) + 1

INSERT INTO #validdatesasints

( date

)

SELECT TOP ( @Top )

CONVERT(INT, CONVERT(VARCHAR, DATEADD(day,

ROW_NUMBER() OVER ( ORDER BY ( SELECT

NULL

) ) - 1,

@ValidDateStartValue), 112))

FROM master.sys.columns a ,

master.sys.columns b

--find offending rows

SELECT *

FROM [Monitor].[dbo].[Job_Monitor]

WHERE LASTRUNDATE NOT IN ( SELECT date

FROM #validdatesasints )

AND LASTRUNDATE IS NOT NULL