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Try out DriveDX to see if there's any problems with your HD, I remember having other Mac Mini's with poor quality drives, one with noise, one was pretty much like yours.

I had a terrible experience with Yosemite on my 2012 Dual Mac Mini, it was slow and laggy and frustrating, so I went back to Mavericks.

Maybe it's some bugs they need to fix or it needs an SSD to boost things up.

Can't wait to get an SSD in mine to be honest, I hate moving drives now.

On a bang for the buck basis the new Crucial MX500 looks like a great upgrade. ~$200 for 512GB.
 
I've got a Mid 2011 mini with 8gig of ram, put a 128gig SSD in.
It was really slow to boot, mainly used as a streaming machine.
The screen used to block out with memory issues.

I put a partition on my external Thunderbolt drive and its lighting fast, runs without any issues...
 
Replacing the HDD is only complicating things with the return process/warranty. Why take the risk? Just take it back to the shop and swap it over. If you have the problem again you know it's probably software or Yosemite install related and can figure it out from there.

I put an SSD in my exact same machine but running Mavericks, and the original 5400rpm drive is great as a second drive. Why go 7200rpm, adding heat into an already relatively 'hot' running machine?

For a backup drive, the 5400rpm 1TB drive is perfect, just whirrs away doing time machine backups, not bother me at all, and not wearing out my SSD :)
 
Update: ran several different HDD diagnostics, all negative. Erased the disk (again) and reinstalled OS X but no third party apps. So far, so good...
 
Yosemite runs very smoothly & fast on my 2009 Mini with 4 Gb RAM and 5400 RPM HDD. So it's not the computer. Possible hard drive failure or initial Spotlight indexing?
 
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