Dropbox has two modes: APP_FOLDER and DROPBOX. APP_FOLDER just creates a sandbox and does not give me permission to all your Dropbox data. I would never want access to such a thing on a server that's publicly visible.
The Dropbox authentication screen says: "This app will create a folder named webcache in your Dropbox. The app will only have access to this folder." But yeah you have no idea what's going to happen when you click that grey Submit button.
I agree the lack of polish makes it look spammy. Maybe some rounded corners and bubbly clouds would make it more trust-worthy. Along with an invitation to come over my house and have a beer.