Write logs from to virtual console to file
 

I boot Slackware directly to runlevel 4 and XFCE. When I switch with ctrl+alt+1 to tty1 I can see many interesting logs from various X apps. However I can't find them later in /var/log/*. What can I do to persist them to some file?

You get output to tty1 after X starts? "Stating X11 session..." should be the last message displayed. Logs from X will be in you Xorg.log file. The boot up messages from tty1 can be displayed with dmesg. You can pipe the output to a file of your choosing.

I have logs in Xorg.log and on tty1 (mostly errors and warnings from gdk, gtk, flashplayer etc). Logs from console does not appear in Xorg.log.

try somethings like

@reboot /dev/ttyS1 > console1.log

in your crontab ?

I can see X.org server starting on tty1. It prints some info about itself, then I'm switched to another console to login window.
X server logs some info to /var/log/Xorg.0.log, but not all of it. Various x-programs log their warning and error messages only to tty1, not to /var/log/Xorg.0.log
So how can I make X server log ALL messages to log file?