I got a 2012 2.6ghz 16gb quad mini with original Apple 256gb SSD a few months ago that I dedicated to video editing. At the moment, my projects all involve legacy 480i60 DV footage I shot of theatrical perfomances 10 to 15 years ago. The mini handles this with no problem of course. For final delivery, I am using Compressor to convert to 480p30 with the highest quality motion compensation. This puts the biggest stress on the machine, a one hour video took about 13 hours to compress.
I also have a 2013 MacBook Air with the 1.7ghz i7 CPU, 8gb RAM and 512gb SSD. The Mini renders video twice as fast as the MacBook Air. It is also twice as fast as my base model 2012 i5 Mac Mini. This is pretty much proportional to the geekbench ratings for these machines. But the difference is pretty significant when you consider that the 13 hour export mentioned above would have taken 26 hours on the slower machines.
I have also done some editing of 1080i60 footage from a Sony HVR-Z1 and 1080p24 from a Sony XDCAM-EX that work fine on the Mini. I still use legacy FCP for my editing, and it is really all I need for the legacy SD footage. But I spent awhile with the FCPX free trial and it ran fine. Also tried DaVinci Resolve and was surprised that it seemed to work well, although I only tried with SD footage.
I don't put any media on the internal 256gb SSD, I have several 5TB external USB 3.0 drives for storage, they clock at around 180MB/sec. To make editing smoother, I have a 1TB Samsung T1 USB 3.0 SSD that I use for my current project. It clocks around 400MB/sec write and 430 read. The internal Apple 256gb SSD gets about 450MB/sec write and 520MB/sec read.
I like having the internal SSD because programs launch quickly and it boots in about 15 seconds. But the external SSD is a pretty good option if you can't find a model with internal SSD and don't want to tear it apart to install. I setup another 2012 Mini for my daughter's family recently using the same Samsung T1 external SSD as a boot drive. it also feels very fast, but it takes 30 seconds to boot vs 15 with my internal SSD.
I am very happy with the quad mini, it's a fast little machine. I don't use any software that needs a better graphics chip so the HD4000 is fine. In fact, i have some legacy CAD software (VectorWorks 2008) that has issues with the newer HD5000 chip on my MacBook Air but works fine on the Mini. I also like the fact that the 2012 Mini runs MacOSX 10.8.5 which makes it more compatible with my old software.