Graphics output on Macs is notorious for dropping strength when there are too many "adapters". That I *know* from experience.
Thunderbolt port is not an "adapter", so the miniDisplay-to-VGA/VGA-cable is a "one adapter" setup.
As to running on two monitors ... I would get a USB-to-VGA adapter for either the VGA display or the projector. Use the miniDisplay-to-VGA for the other. And given the power draw for two monitors on a small-ish macMini power supply, a powered-USB-hub will help alleviate the power draw.
As to the "embarrassment factor" for so many adapters, you can smile contendedly when another's Windows-based computer shows a pretty "blue screen" during a presentation.
As long as the USB-to-VGA is not damaged, it can be returned.
I tried to use my Mini with the Thunderbolt to VGA thing, but finally gave up. I had to unplug/replug often coming out of sleep.... I just got tired of screwing with it and got a DVI cable, and used the Apple included HDMI to DVI adapter. All problems solved, and the desplay looks better. I have a 4 year old 22 inch monitor with a VGA and DVI input. I just didn't want to spend the money for a cable...... glad I did.....
That will solve the montor issue.
But running both a monitor AND a projector is on the "required" list.
I did not read in your response where 2 devices are supported.
But then my eyes are old and it is 11:15 PM here ...
A lot of LCD projectors have a pass-through VGA port. That is they accept a VGA input from a computer and obviously use that to project an image, but also have a VGA output port which can be used to connect to a VGA monitor. I suspect the original idea behind this was that the person doing the presentation would be facing the audience and the project might be projecting to a screen behind the presenter. By having a monitor in front of the presenter he/she would be able to see what was being projected along with the audience without having to keep turning round.
These days this is not often a needed feature because most people use laptops with built-in screens to connect to a projector and the laptop screen does the same job.
Can the HDMI port drive analog displays (VGA displays for example) using adapters?
No. The HDMI port will drive digital connections—such as DVI—using the adapter that came with the Mac mini, but cannot be used for analog displays such as VGA. You can purchase a Mini DisplayPort to VGA adapter separately to drive analog displays.
from here http://support.apple.com/kb/HT4214
Yes, I have a apple tv going to my VGA projector, I bought a HDMI to VGA converter from a website called avdemand it worked great. It also broke out the audio so I could go to my sound system as well here is the link http://www.avdemand.com/HDMI-to-VGA-Converter-p/cthdmi-vga.htm