For what it's worth here's my experience on this issue. I still have my original Lumia 1520, purchased on release day (USA).
With WP 8.0:
Didn't have any screen sensitivity issues until after Glance was released and I activated it. With Glance turned on, I only had the sensitivity issues with the lock screen (using a PIN) once logged in, I would very rarely have a random tap while using the phone. The behavior on the PIN lock screen was like if someone was tapping the screen dozens of times very quickly. I found that if my held my thumb on the delete button it would "tap itself out", and stop acting up after I held my thumb on the screen for about 4-5 seconds.
After disabling Glance, I no longer had issues with the lock screen and very rarely (even less than before) had a random tap on my phone once logged in. With glance off I'd say I'd notice a phantom tap once every 3-4 days, and it would be one tap and done.
With WP 8.1 Developer Preview:
I have not experienced any screen sensitivity phantom taps at all since installing WP8.1 through the Developer Preview. I have not tried activating Glance again though, and I haven't missed the feature at all so I don't intend to use it going forward.