Are said spots black? Or simply not responsive to touch?

Here's my suggested process:

Clean the display with a microfiber cloth.

Apply one or two drops of 90% isopropyl alcohol directly to the cloth then wipe the entire display and dry with a different section of the cloth.

Test again.

Close all open apps.

Next reboot the device several times.

Ensure your battery health % found in

Settings > battery > battery Health and charging

Is over 80% anything under 80% can cause the iPhone not to function properly.

Inspect the display for psychical damage.

If the display appears good as new but doesn't take touch in a few places or the entire display and displays an image over the entire display.

It could need it's fpc flex cables re-seated.

If you wish to try a hardware repair like this I suggest following a good guide to the tee.

For a reseat on the display connectors pause on removing the display from the phone and follow the directions in reverse.