I do believe Intel HD 4000 graphics support OpenGL 3.0 3D graphics engine so I don't believe the 3D would be an issue, after all, you're running an operating system's 3D graphical user interface, not playing the latest installment of Crysis or Call of Duty!
Having said that, I've also had a slow and buggy experience with my nVidia 8800 graphics card (that had no problems with any version of Windows or with Ubuntu 12.04) so my guess would be that it is a graphic card driver/Unity issue.
Perhaps you could try
While I do agree with you about 3D graphics support not being an issue I have to say I am currently trying out xfce desktop on Ubuntu and it seems quite fast, responsive and more stable than Unity.
sudo apt-get install --reinstall xserver-xorg-video-intel