Lots of folks are using Rain-X on their screens to cut down on smearing and it seems to work pretty well. Just about any auto store carries it as an auto windshield treatment.
On the subject of screen protectors, I had one on my A500 and didn't like it. I could never get it to be super flat. There were 6 or 7 perfectly straight parallel lines going from end to end that i couldn't get rid of. I've seen other posts about that so I know I'm not crazy The only advantage I saw was the slight tackiness it gave to the top of the unit...made it slightly easier to hold. I left it on for about 2 weeks and then got tired of it and took it off. Now my screen has a couple of minute scratches but I don't really mind. To me, devices are to be USED, not babied, beyond being careful not to drop it or spill stuff on it, but that's just me...YMMV
I'm using one that is great but it took a couple of week to become clear it took ages to smooth out the air bubbles but its worth it now.
It does make the tab easier to grip too.
Using recommendation from other posts, I ordered screen protector from www.posr.us and have been very satisfied with it. The big thing with any protector is to no only make sure the screen is free of prints when you apply but also make sure there is no dust on the screen. I used 3" carton sealing tape to gently wipe across the screen to remove the dust. Protector reduced the glare and fingerprints are not as noticeable. Very satisfied.
As Spider recommends, RainX works very well!! Futhermore there are protective films available on Amazon and other tablet accessories sites, just for the Acer A500.
I just got some cheap screen protectors off eBay and they have worked fine. No smearing, no bubbles, very easy application. I figure I'd rather buy one and not need it than not buy one and end up wishing I had.