I found this thread googling 'toddler screaming in night', because I am being seriously disturbed by my neighbours, too.
In fact, I am here now because their daughter started screaming at 3.30am, and was left screaming til 4am, by which time I was wide awake. (So was my 10yo, by the way - but luckily he went back to sleep easily after a bit of a moan about 'that bl*y baby'!).
She screams a LOT more than my boys did; but what bothers me is not really her screaming, but the fact that she isn't comforted. I do find it hard to understand how parents can leave a child so distressed for so long. Mine got comfort when they cried.
I have spent a lot of time over the past couple of years worrying about whether I might be ignoring abuse that I should be reporting. Logically, I know it is not abuse; but when you have been listening to hard-core hysterical screaming coming through the wall for 20, 30, 40 minutes it becomes harder and harder to think logically. I'd quite like to go round there and give the child a cuddle myself, but of course that's impractical at 4am, and impossibly offensive.
It has helped a bit to be reminded that toddlers do scream a lot... But it does seem hard that I have to live through these kinds of sleepless nights again, and it's not even my kid! I'm at risk of becoming badly sleep-deprived, with a teen who's up til just before the neighbour's child starts screaming, and a 10yo who wakes up not long after she stops! :(