I find it insanely hard to believe you've received 3 defective imacs from apple. This is usually a case of user error when such a streak of bad luck comes from any product.
As for mini's humming. Which mini? the 2011 mini running at maxed cpu is pretty much silent. I think the highest I've seen the fan was like 3800 rpm and I was astounded to see it get that high. only then was there any perceptible noise from it. Do you keep your macs in poor ventilation?
You don't work for Apple, do you?? These are the same things they are telling me (that it's user error). But here's the synopsis:
First iMac - seemed perfect, except Target Display mode failed to work. Screen would flicker blue, and then just settle to black. The MBA I was connecting to the iMac is showing the iMac as a screen in Display Arrangement, but I could not actually see anything on the iMac. (And yes, I tried raising the brightness to no avail.)
Second iMac - Connected immediately to the First iMac and initiated Target Display mode (Second iMac was a second screen to the first iMac). This worked. Left it this way and used both iMacs for a few days and started getting horrible image retention (would take hours for it to fade away and not be noticeable).
Third iMac - Having sent the First iMac back, but retained the Second iMac, I immediately set up the Third iMac as a second screen to the Second iMac. This worked as well (or at least I think it did), but then I started noticing image retention on both iMacs. Connected an iMac to my TV and still noticed IR issues on the iMac (note - I believe IR is exacerbated by the use of a second display, be it a monitor, TV or another mac in Target Display mode). Then, after switching the Third and Second iMacs around on my desk (moving the second one to be on the left and the third one to the right) Target Display Mode stopped working again (or so I thought)...
2012 2.6 i7 Mac Mini - Enter the Mini. Having packed up the Third iMac and leaving the Second iMac on my desk, I connected the brand new Mini to the iMac and initiated Target Display mode, and BAM, nothing. Screen flickered blue, but dropped back to black with no backlight. This time, I had some windows open since it was now the main display for the Mini, and I noticed I could see the outline of different windows. Looking closely I could see that technically the iMac was working, but no backlight was on to actually display the images. Talked to Apple support a number of times and they are still working on it. I moved the iMac back off to the left side of the desk again and set the Mini up in its place. Tried Target Display mode again a few days later and it WORKED! But why its hit or miss is a mystery still.
Unless Apple really isn't supporting TDM or using an iMac with a second monitor, I don't think it can be user error. I will note that I have a Tewlvesouth HiRise stand that the iMacs are sitting on, and unless that is causing some kind of grounding issue, I can't believe that is to blame at all.
As for the Mini's hum, it sounds more like a power supply hum (or maybe HDD). The fans top right out at 5500rpms on Handbrake since the Mini has poor ventilation as many have noted. Don't get me wrong, its a very powerful machine, but being 2 feet in front of me those fans are like white noise generators and I can't take business calls while sitting right in front of it.
Any of this sound like user error? (Seriously, am I doing something wrong??)