The XFree86 X servers will produce a lot of diagnostics output on stderr during startup. This output will be lost after the server reached a certain point in its console initialization process. You should redirect stdout and stderr if you want to analyze the diagnostics produced by the server.
When the X server is running output made to other consoles will be lost. After server shutdown the screen contents of other consoles may be inconsistent with what one would expect (i.e. random).