Dust cover up or down?

Off

Goes without saying. Off!

Down. To prevent dust settling in the record.

If you are in a fairly dust free environment, then, you could leave it up for convenience.

For me in industrial Singapore, I see benefits from keeping it down.

I have a Technics 1200G.  I've always played with the cover down.  For my own satisfaction, I'm going to try with it up and off to see if I can hear a difference.

A proper dust cover is a big plus for a turntable both sonically and for protection for records and tonearms. What is a proper dust cover?

@herbreichert has notice no problem with his Linn. @fbgbill I do not know if you think a Sota Cosmos is a high end turntable but it does have a dust cover and like Herb's Linn the Sota's dustcover is isolated from the turntable, tonearm and cartridge which are floating on a separate sub chassis.  That is the most important criteria for a proper dust cover. It can not directly transfer vibrations to the working parts of the turntable. Used like this a dust cover actually improves the sound by attenuating the sound that gets to the cartridge like wearing ear muffs. In a system with Electrostatic speakers the improvement in detail is noticeable. 

This leaves a lot of turntables out in the weather but, there is a solution that can be used with any turntable. You have a baseplate made that is larger than the plan view of the turntable to which you can hinge the dust cover. The baseplate could be made out of wood, acrylic or even granite. There are plenty of companies that can make a dust cover of any size. You place the turntable on the base and the dust cover closes over it. I'm surprise there is not a company that makes the whole rig.

I am not the only one who thinks this way about dust cover. In an email conversation with Mark Dohmann he related that he was working on such a dust cover for his Helix turntables. 

@jagjag , unless you live in an industrial clean room there is no such thing as a dust free environment. Another issue is there is no such thing as a static free record. There is always a slight charge on records. Even if you ground out the record with a dead short within a short period of time the record will develop a charge. Why? The paper label and PVC are at opposite ends of the triboelectric series. Electrons migrate from the paper label to the vinyl giving the paper a slight positive charge and the record a slight negative charge, more than enough to collect dust. During play the record also develops a little more of a charge.