Dreamfall: The Longest Journey is a game with some years on its back and as such the 3D engine lacks a lot of the tricks modern engines use. Fortunately, some of these can still be used if you are running the game on an (newer) Nvidia graphics card (Radeon cards may have similar options). Here's how I did it:

1. First tweak the in-game settings to match your system
   
2. Open the Nvidia Control Panel (right-click the Nvidia icon on the taskbar)
   
3. Goto 3D Settings -> Manage 3D Settings -> Program Settings
   
4. Select Dreamfall: The Longest Journey from the drop-down list
   
5. Set Anisotropic filtering to 16x
   
6. Set Antialiasing - FXAA to On
   
7. Set Antialiasing - Mode to either Enhance the application setting or Override... depending on your in-game settings
   
8. Set Antialiasing - Setting to 8x
   
9. Set Antialiasing - Transparency to 8x (supersample) (this may not make any difference)
   
10. Set Multi-Frame Sampled AA (MFAA) to On
    
11. Apply the settings and run the game to enjoy the enhanced graphics

Depending on the speed of your card you may need to tweak some of these settings. Personally I find that antialiasing and texture rendering improves dramatically with these settings.