Versions 2.24 and 2.25f both have alpha status demo recording:
Demo recording is only server side at the moment. This is easy for single player as you are automatically the server, but for multiplayer you need to be running the server, or at least know the person and persuade them to record a demo.
Demo playback a bit buggy, and is only really working in Chasecam and Freecam modes, there is a command for first person demo playback, but it's jerky and buggy. In single player demos, moving objects don't appear until they are in use, and some sounds are missing (2.25f is worse for this). Also the maps need to be loaded before playing, otherwise the start of the demo is lost.
In deathmatch demos, playback seems much better, you can Chasecam all players (cycling between them using the "fire" button), and moving objects and all sounds are present.
The console commands for demo recording and playback are:
"demorec 'demoname'" - to record a demo called 'demoname'
"stopdemo" - to stop that demo recording (it seems you must do this before recording another demo)
"demoplay 'demoname'" - to playback the demo called 'demoname'
I have quite a few demos at my site below - speedruns and a few LAN DM demos too...
Unreal, Na Pali and custom map speedrun demos at
TEAMShambler FPS Demos and Discussion
The Shambler also reviews Unreal SP levels at
Nali City