OSX ventura installation "this disk has S.M.A.R.T errors" message

An alternative to having the internal disk replaced along with the labor costs would be to get an eternal SSD, clone your boot drive to it and run on it. I have a couple of eternal SSDs that I boot into to run other systems. If you go that route you'll be able to take the external drive with you when you finally upgrade your iMac at a later date.

If you go that route I recommend you contact OWC (MacSales.com) Customer Support and see which of their many offerings would work best with your particular iMac, workflow and budget.

OWC is considered by many to be the premier 3rd party hardware supplier for Macs.

That being said I would still take it in to the nearest  Apple Genius Bar for a free diagnostic check to confirm the problem.

Back up your data.

This backup is the first and foremost priority here. No other steps, no tests, no diagnostics, no re-installs, and no other operations should be attempted prior to obtaining as complete and current a backup as can be acquired.

Then run Diagnostics.

Then contact Apple Support and discuss your options and alternatives.

If this Mac has a hard disk, I’d be included to discuss replacing a hard disk with an SSD, too. Apple won’t do that, but an Apple authorized third-party repair provider might.

A little confused. What exactly is your advice/suggestion?

If you think it is fine because the diagnostics came back clean, go ahead and use it.

Ventura won’t install because of them as doing anything with that disk could result in failure any time.

Separately, isn't it a bit odd that it takes a Ventura install to discover a SMART error?

Disk Utility should report them, too.

They have tools which can diagnose drive problems much more thoroughly than the First Aid of Disk Utility or the build in diagnostic features of the systems.

They may more than likely want to erase the drive and install a fresh system to make sure it's not software related. So make sure you have a full and current backup of your internal boot drive before going in.

If you have to carry the iMac a long distance and you can temporarily double park in front of the Apple Store do so, run in and have an employee carry it in while you park. I've done that a couple of times.

I’d still contact Apple Support.

SMART errors usually mean the device is failing.

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SMART indications don't mean the drive is bad. They indicate impending failure.

But, continue as you wish.

I would assume your visit superfluous. IF you start recording SMART errors, I would consider the drive circumspect.