If you click the smart tag that appears to the left of the error, you can see Excel's complaint:
As you can see, Excel is complaining that you have a date in Text format that has a 2-digit year. Excel sees this as a problem because it is ambiguous whether 6/2/16 represents the 2nd of June 2016 or the 2nd of June 1916. As you can see, it is offering to convert the date into one of these two formats so that it will no longer be ambiguous.
You could eliminate the ambiguity by adding the full year to each of your dates, but the best solution to this would be to convert your textual dates into 'true' dates (ie. date serial numbers). A date serial number never has any ambiguity about which date it represents.
You'll remember that date serial numbers are explained in great depth in the video lesson: Expert Skills Lesson 3-7 Understand Excel date serial numbers and custom date formats.
You can also see how to use the DATE function to convert text into date serial numbers in the video lesson: Expert Skills Lesson 3-11 Use the Excel DATE function to offset days, months and years.
I have attached a copy of your workbook with the textual dates replaced with date serial numbers:
menu with error icon datefix.xlsx 11.94KB
An alternative solution might be to switch off Background Error Checking, which will stop Excel from automatically displaying error icons. However, this will be saved with your copy of Excel and not with the workbook, meaning that it will affect all workbooks that you open with your copy of Excel. It may also cause errors to be hidden that you'd prefer to be alterted to, so I wouldn't recommend doing this.
If you do want to switch off Background Error Checking, you can see how to do it in the video lesson: Expert Skills Lesson 4-12 Manually check a worksheet for errors.
I hope this solves the problem, but please feel free to reply if you continue to have trouble.