1. Set your account's profile timezone to differ from the server (I created a new OnDemand instance set to US/Chicago then set my profile to Australia/Sydney).
2. Start a new basic search, add Due Date to the fields.
3. Select "Date between" and choose two different dates (say, 2nd April and 6th April).
4. Save that filter, then reload the page.

The dates will have changed to 1st April and 5th April and are saved directly in the database with these values. Advanced Search in unaffected, this only occurs with Basic Search. It doesn't occur if your profile timezone is set to the same timezone as the JIRA server is (be it by manually selecting the same timezone or choosing "JIRA default").

I've been able to replicate this in SAC as well.