Some methods I've worked out over the years of working with crappy scanners:

1 - I haven't seen a flatbed scanner yet that scans all the way to the edge - it usually trims off a tad at the edge. I scan a flat ruler or graph paper to see how much margin I need, then cut a guide out of heavy white pasteboard (the stuff they wrap shirts around is pretty good), and tape it to the scanner - so I have an accurate edge.

2 - I don't even bother with the cover - half the time, closing the cover nudges the artwork out of allignment. I use about 80 sheets of paper as a cover - it rolls on, so I can hold the art in place while I'm putting it on, then hold it in place by pressing down on the paper where it's down as I take my hand out. (Not the best description of the process, but I think I understand it :) )
Then I use some very hefty, small weights on top of it to really flatten down the spine. Being the nutcase I am, I use boxes of ammo - the 50-round boxes weigh surprisingly much. Cans of vegetables would probably work as well - anything that'll press down hard enough to take the final curl out of those spines.

Danno the pontificant