Are there a lot of plain edge dollars floating around? Would it be worth sifting through rolls at my bank looking for them?
If you can get uncirculated rolls of Washington dollars, yes. Adams plain edge dollars are much more rare. No reports I'm aware of of Jefferson plain-edge dollars.
I got a roll of the Washington dollars back around the time when they first came out and some coins (more than half actually) had the lettering on the rim upside-down and some were regular. Is this considered an error by any means?
Actually that was a big ebay scam when the Washington first came out people where selling "Upsidedown" edge lettering dollars. The mint issued a statement that the lettering is random.