That non closed cube have all blue faces doubled and having same normal. So you can notice it only if you turn on idexes and see sort of hard to read index because it’s two numbers at once. You get no other indication.
Contrary to 3d max for example where edit poly is fool proof and just doesn’t allow you do make such geometry, in Blender you can do so easily with such not closed cube just by shift+D with auto merge on accidentally and never notice you did it.
Is there a way to check and fix it? A simple easy way?
I don’t quite understand… if you have automerge off and duplicate some geometry with Shift-D… then it "sticks to your mouse pointer " until you press return or right click… even if done this accidently then there is the Adjust Last Operation menu which shows you Add Duplicates… and this is what you have done then… if you don’t move, rotate, scale them then it’s also your choice…
So blender exactly does what you are telling it…
…finnaly looking at you statisics there is also Mesh → Merge → By Distance…
…or be sure that auto merge is on…