What's the difference between "overlook", "ignore" and "neglect"?

It seems these words all mean you didn't pay enough attention to something.

Solution 1:

Overlook is normally by accident
I was not paying attention, so I overlooked the mistake in my spelling.

unless you are being nice and allow someone else's mistake on purpose
You are clearly sorry you are late, so I will overlook it this once

Ignore is by intent
I saw the spelling mistake but chose to ignore it.

Neglect can be either, but implies deterioration of the neglected and that it is something you should have done.
I was supposed to use a spelling checker but neglected my duties
He was so busy on the computer all night, that he neglected his health and his family

Solution 2:

They connote different states of culpability in the act of not attending to something for a given individual they're describing. To overlook something is to not attend to an object, by forgetting to do so for some trivial reason. To ignore something is to not attend to an object, and to deliberately do so for a considered reason. To neglect something is to not attend to an object, not only deliberately so, but immorally so, perhaps even tortiously so.