Points won't snap/Alignment is off

[RustleMeNot]

OK, I'm normally pretty good about finding solutions to my illustrator problems (by finding solutions, I mean entering my issue into google), but this time that approach won't work.

I have two problems. the first problem being that Illustrator absolutely INSISTS that these two shapes shown are perfectly Aligned in the center
(All I did was copy one, past in place, moved it next to the original object, and delete it's left side; so, both of the objects shown are the same exact dimensions).

The second problem is fairly small, but I don't know how to word it effectively so I can track down a solution elsewhere; Illustrator is certain that the following two points are joined, when they clearly are not:

Any help with these issues would be appreciated.

[Monika Gause · Accepted solution]

Can you turn off the pixel perfect alignment and try again?

Create pixel-perfect designs |

[RustleMeNot]

Thank you. That's one problem solved.

[Marley C.]

This is exactly what I came here for. Thank you!