ATI responded back to me pretty quickly.  However, the message was useless, stating simply to use the latest drivers, which of course I was.  I responded again and just restated the same problems as follows:

I have installed the latest drivers but I'm still not having any luck. With a single card in place, everything works wonderfully. But when I put the 2nd card in (they are identical cards), the quality of the display drops significantly to where it's unusable. Moving windows around does not force a redraw, popup windows are not displayed correctly, etc.

What is the recommended usage for 2 of these cards on a 64-bit AMD Windows Vista machine? Should I be using only the DVI ports, or should I be able to use the DVI and VGA ports to achieve dual monitor support? I am trying to run 3 VGA monitors.

Thanks,
Jeff

Here's the response that I received this afternoon:

Hello Jeff:

Thank you for contacting AMD Customer Care for ATI products.

Please be advised that using two Radeon video adapters (or one Radeon and one third-party) in one system (with the exception of Crossfire setups) is neither recommended nor supported due to resulting hardware and software conflicts.

For multiple monitor support (more than two), please refer to the ATI FrieMV 2400 series. More details are accessible at:

http://ati.amd.com/products/firemvseries/index.html

Regards,
AMD Customer Care for ATI Products

This is not at all what I expected them to say, and my message back explains why:

Thank you for the response.  However, the reason I selected these cards was because of the touted support for dual cards to drive up to 4 monitors.

http://www.visiontek.com/products/cards/retail/x1300_256pci.html

On that page, the following is stated:
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Advanced Multi-Display Capability
VisionTek’s Radeon X1300 PCI card brings advanced multi-display capabilities to your personal computer.  Easily connect and run two (2) displays simultaneously using a single X1300 card, from VisionTek.  Achieve your maximum productivity by running two (2) separate applications, when utilizing side-by-side dual monitors on your desk top.  Add two (2) VisionTek X1300 PCI cards to your PC and manage four (4) or more monitors at once.
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This same information is highlighted on the product packaging.

Is VisionTek advertising a false claim or can dual cards be supported to achieve 3 displays?

Also, I contacted VisionTek's support on December 21, 2007 and I have not yet received a response which is why I've escalated my support to you.

I'm sure their next response will be interesting.