I was a bit disappointed with the Scrabble price on the iPad. It's not that bad for software, but the iPhone version works pretty great on the iPad which doesn't make it very worthwhile to pay $10 for an iPad version. It is a little pixelated, but very playable.
I would think you can play solo since you can on the iPhone (I think it's the Play Now on the 5th screen shot in the App Store).
I do like the looks of their party mode if you have several people around the iPad who have iPhones using the free Scrabble Tile Rack. That's a really interesting concept!