Regardless of what people say, non-trivial Latex documents involving mathematical notation or code samples almost always require last minute tweaking because the math or code environments don't wrap correctly and make ugly things occur.
It would be very useful during the final phases of document preparation, when you do care what the rendered document looks like, to have a "debug mode" consisting of a split panel window with one side containing the DVI viewer of a constantly updated render of the paper alongside the LyX editor. I guess since some people hate split panel windows, it might be a good idea to have an option to have two separate windows too, as it is now, but with the added synchronization features, such that the rendered paper is constantly automatically updated and the scrolling is locked between the DVI viewer and the LyX editor. So if I need to tweak something I see as I am flipping through the DVI viewer, the LyX editor is automatically scrolled to that part of the document. Currently the DVI viewing behavior is very unproductive as it requires the following process: 1. ctrl-D 2. resize/zoom DVI viewer so that things aren't microscopic 3. page down in DVI viewer to check for ugly things 4. scroll in LyX to corresponding location 5. make changes 6. close DVI viewer 7. goto 1 A split sync'ed panel or sync'ed double window approach would be much more productive, and that is the entire point of LyX to begin with: improve your productivity. I love watching people hand edit Latex documents and spend lots of time figuring out where their syntax error is... that or trying to remember a certain command. I keep telling them to give LyX a try. thanks, luke