If you want to query the dates statistics were last updated on your tables, this should do it for you.  Just adjust the WHERE clause to limit the query to...

I have to ask if there's a pattern for which days are good and which ones are bad.
Also, does it correlate to any statistics maintenance or periodic data loads...

I think you're picking the simplest approach by using SQL, but you can definitely define different passwords.  Here's a very simple demo, just varying the password by a number, but...

It looks like you already have your answer.  For future reference, Lynn Pettis has a great list of common date functions at http://www.sqlservercentral.com/blogs/lynnpettis/2009/03/25/some-common-date-routines/.

To check your network latency, you'd talk with your network administrator.

How's the query performance if you run it from a different workstation?  When I say that, I mean...