After using a Galaxy S3 for almost 2 and a half years, I found that the AMOLED screen on my particular phone is susceptible to screen burn in. I use Waze (a mapping app) whenever I drive which. I would say that on a weekday, Waze is running about 60 minutes per day on a weekday and about 2 to 3 times that on a weekend day. After less than a year, I started to notice image burn in on my screen. The areas where the Waze screen is white and borders on the areas where it is dark can be clearly seen in less than a year.
Initially after less than a year, I only notice it on the title screen of Yahoo Weather because it displays a mostly one colour title screen. For images with pictures or where the screen is not one solid colour, I didn't notice. After around 2 years, I can clearly see these ghost images if I know where to look.
The ghost images do not actually hinder my ability to see information on the screen. It's just that part of the screen is slightly brighter than other parts. These slightly lighter and darker areas show the ghost image of the Waze navigation screen I use when driving.
I suspect that each pixel gets dimmer over time when it is used a lot. The Waze navigation screen has some dark areas, but mostly white areas where the map is shown. The dark areas are where the estimated arrival time is displayed and where the icon is that shows my location on the map.
I haven't heard of this issue with LCD screen. The backlight lights up the whole screen and the pixels just block light.
I don't know if there are any tests that any reviewers can do in a reasonable time after the release of a phone that can measure how bad the burn in effect is on screens. It took close to a year of use before I started seeing it. Maybe if they kept the phone on 7x24 for a few weeks, they can really test this effect in a timely manner after a phone is released. So far, I have not seen any review of a phone ever mentioning any screen burn in effect on any phone.
It's been over 2 years since the Galaxy S3 was released. Perhaps AMOLED displays have improved over that time to dramatically reduce screen burn in.