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Describe the Bug:
Eye of Singularity's first ability (ETB) seems to work fine. The second ability seem to only affect basic lands to a certain extent, though:

1) When a permanent other than a basic land enters the battlefield while Eye of Singularity is on the battlefield, other permanents with the same name are not sacrificed (tested with Jungle Wurm and City of Brass).

2) When a basic land of a certain type enters the battlefield for the first time since Eye entered the battlefield, all other basic lands of that type will be destroyed.
However, consecutively played basic lands of that type will not trigger that behavior, which might be due to bug 3.

3) Basic lands that enter the battlefield while Eye of Singularity is on the battlefield, receive a prohibition sign which not only makes them untargetable for the rest of the game, but also makes the game handle those lands as if they were not on the battlefield when it comes to other cards checking for them.
For example, Flashfires doesn't destroy Plains with prohibition signs on them.

Which card did behave improperly ?
Eye of Singularity

Which update are you using?(date,name)Which type(Duel,Gauntlet,Sealed Deck)
KOT, duel

What exactly should be the correct behavior/interaction ?
Eye's second ability does affect permanents otehr than basic lands and does not affect basic lands.

Are any other cards possibly affected by this bug ?
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Fixed in 8a72191

generally works, but...

In the attached save, debug an Air Elemental into your hand and cast it. The Eye of Singularity will trigger and kill everything in play. Huh?

Another instance of Eye of Singularity killing every permanent:
I had in play Flagstones of Trokair and played another one.The legend rule triggered as it should.I selected then to keep the old Flagstones of Trokair and the new was sacrificed to legend rule.I put a Plains in play with Flagstones of Trokair ability.Then Eye of Singularity triggered and killed everything on board.

If you select to keep the new Flagstones of Trokair and sacrifice the old to legend rule then everything works fine.

If my conclusion is correct it seems that if Eye of Singularity doesn't find the permanent that just entered when it triggers then it destroys everything.