Bought a brand new (i.e. not refurbed) Lumia 620 yesterday (9/6/2013). After charging the battery then turning the device on for the very first time, going through each setup step and so on... then when it came to the time zone setting, e.g. UTC, London etc. the screen went mad and looked like the screenshots in the first post of this thread, as in the screen was all repeated over itself. Althought totally unreadable to us humans, the phone seemed to think nothing of it and it still seemed to respond to scrolling and selection. Interestingly enough, clicking randomly on the screen to choose a time zone, though i could not read the time zone, and then clicking back into the time zone selection, the screen was still messed up - but not on the previous page. Locking the screen and then unlocking the screen seemed to cure the issue temporarily and so I was able to finish off the setup process, albeit having chosen a wrong time zone.
Having had that as a first 'welcome' to WP8 and Nokia Lumia Phones... not a good start at all.
Following on from that first screen error event, the screen did a similar thing again on the lock screen, where the time and date and other text is written - it was all messed up again, but the actual background photo looked ok.
Between the two errors I'd not installed any apps or done any entry of data, it was and still is just as new, but unboxed so there is no software that I'd installed causing the issues.
5 minutes into owning the phone, checked for firmware updates using the phones built in check and it did find one. Having successfully updated the phone, the screen unlock messed up text issue has happened again three more times, so the phone is going back to the shop. Not a good 24hour start to Nokia Lumia ownership and I'm tempted to send Nokia a bill for doing their Research & Development for them, plus fuel to take it back to the shop!