File uploads (<input type="file" />)
The browsers currently do not allow you to style the file input in any meaningful way, without resorting to insane hacks. You can't start in a user's home or documents directory. You can't filter to only allow graphic files to be uploaded to a graphics site. You can't choose multiple files. You can't choose a directory to upload the files in it. You definitely cannot drag files and drop them on your webapp.
More and more, the webapps are the applications users interact with the most. Webapps are used as word processors, calendars, spreadsheets, presentation builders, photo editors, photo albums, and more. And as it stands, every browser that I am aware of is fundamentally broken in this one regard.
Who wants to be the first to fix it and make Dethe happy?