--- Operating System, Graphics card ---
Windows 7, no graphics card (the issue is not related to either factor)
--- Blender version with error, and version that worked ---
All 2.5x and later versions have this behavioral problem.
--- Short description of error ---
When VSE is set to "Both" view (mode), Blender should split the window and show both views ("Sequencer" and "Preview") simultaneously.
Instead, it shows the "Sequencer" mode (view) ONLY. To a new user, this is confusing (looks like the command failed).
Further, the user is expected to drag a tiny + button downward from the right-hand-top corner of the window.
Here, another unexpected thing happens: As soon as he drags the button, the "preview" panel springs open and occupies the WHOLE window.
The user cannot see the "preview" view at all.
(Expected behavior: When the user drags the + button, the dividing line between the "Sequencer" and "Preview" views would be dragged smoothly, so the user can set the panes for both views exactly as he likes.)
Instead, Blender has a strange way to make the "Sequencer" view visible: The user has to grab the lower wedge of the window and pull it down.
As the entire window re-sizes, the "Sequencer" view opens gradually.
This also is very odd behavior.
--- Steps for others to reproduce the error (preferably based on attached .blend file) ---