Stats shown are to-date stats from WordPress collected via Jetpack Plugin starting from mid of 2011 (anything prior to that isn’t counted). The post view number is not synced in realtime. Instead, these stats are randomly updated locally using WordPress Stats View Counter plugin. Hence, you may not see any number showing up or an update sooner than one hour.
Speaking of validity based on my experience, the stats could well identify bots to be different from real hit coming from desktop browsers while also excluding visit count of the admin logged-in.