Blue screens are rare, and are most often related to problems with the operating system rather than the program.
That said, your biggest challenge is that you're using this 32-bit program on a 64-bit operating system. This is particularly a problem with Windows 7 because most of the 64-bit drivers for the OS are not yet compatible with 32-bit programs.
You can try going to the ATI or nVidia web sites and ensuring you have the latest drivers for your video card. That often helps. You should also ensure you have the latest RealTek drivers and Quicktime. You should also regularly go to Windows Update and pick up even the non-critical updates.
But, on 64-bit Windows 7, there are still no guarantees at this point. (This can be particularly challenging on VAIOs because Sony has a nasty habit of customizing the operating system.)
Especially with a BSOD, something is wrong at the system level. It could be the OS, or hardware.
This ARTICLE will give you tips on finding out what is going wrong with your system, when the crashes occur. You will have a lot of warning and error messages in Event Viewer. There will be "clues." Be especially careful to check every error, or warning message with a link - those links will likely point you in the right direction.