What else does Apple Care no longer cover on iPhone?

Do you have Apple Care or Apple Care Plus?

There is a difference.

Apple Care is an extended warranty and phone support.

Apple Care Plus also covers accidental damage.

A 3rd tier with theft and loss protection is also available.

That said, if the display is scratched, but not broken and is still functional, that's considered cosmetic damage and does not warranty replacement by apple at all.

Term and conditions depends on the country where you bought the iPhone, usually it covers accidental damage, pick up your country

Legal - AppleCare+ - Apple

If you're in the U.S., here are the Terms and Conditions for AppleCare+ for iPhone.

AppleCare+ Terms and Conditions (U.S.)

It is not insurance - it is a warranty extension.

From Apple's description:

Warranties cover events that are somewhat expected, such as the aging of appliances and systems. Insurance by contrast covers unexpected events that lead to damage.

As Bob Timmons stated above, deep scratches or similar physical damage would not be covered by AppleCare+, but might in fact be covered by insurance if some third party were to provide iPhone insurance.

UPDATE- OK, there is in fact some accidental damage provision in the AppleCare+.

Are they just cosmetic scratches, or are do they affect the function of the screen in any way? Cosmetic issues are not covered by AppleCare+.

There isn’t any Apple Care, the options are between Apple Care+ and Apple Care+ with theft and loss, terms depends on the country where you purchased them

it's an insurance, and covers accidental damage

AppleCare+ covers you for repair or replacement of your covered Apple device in the event of accidental damage with each claim being subject to a policy excess.

It's an insurance policy, as described in the Insurance Product Information Document, an insurance policy underwritten by American International Group UK Limited (AIG), in US AppleCare Service Company, Inc, in Australia is AIG Australia Limited just as examples for other countries read the term snd conditions available on the website

Yes to extend your cover, for the iPhone and for any other electrical you can "extend" your cover with an accidental damage cover underwritten by an insurance company. All damages are covered except minimal damages that do not interfere with the functionality of the device.

It's an insurance

We can't see your phone to offer an opinion, but physical damage is not going to be covered by AppleCare.

Deep scratches did not appear by themselves.

And by the way, AppleCare is not insurance.

AppleCare is Apple’s terminology for the standard warranty.