I think you have a clear sense that her academic/fact knowledge is way ahead of her social abilities. That's not abnormal at all - it's just where your particular child is. And it was clearly a good decision on your part not to push her ahead into kindergarten.
I would absolutely not call the other child's parents. That is not appropriate, because it is the teacher's job to handle classroom infractions. I'm also not sure that the teacher should have told you which kid was upset - and the parents might be concerned that the teacher is sharing info about their child with another parent. So steer away from that entirely.
The simple message my husband has always given to kids (and to adults who need a reminder) is this: "No one ever learned anything while they were talking."
So, your daughter is paying attention, yes, but she's just waiting for someone to make a mistake so she can correct them, instead of listening to take in all the other info in the story or the lesson. So she is critiquing the teacher's speech without realizing that the teacher has a reason for pronouncing a word in a certain way. This is a reminder to all of us not to judge others. The teacher says she didn't mind, but I think maybe she should. She doesn't want you to get all upset about the teacher's feelings BUT someone else (especially a child, but not only that) shouldn't have to hear about it just because your kid noticed it.
Being helpful to others is one thing. Being bossy, pointing out errors, or criticizing the way in which another person learns is not okay. So teach your daughter, over time, that people may do things in different ways and they learn in different ways. For example, there is probably a big banner in the classroom with the alphabet on it. But we also sing the "ABC Song" all the time. Why? Because some people learn visually ("by looking") and some people learn in an auditory way (by hearing, singing). Others are tactile learners and take in info through touching or going through certain motions. Another example - it's one thing to watch someone ride a bike or do a somersault, and it's quite another thing to actually do it even if you "know how." So point out to her that the child who E thinks can't do something might be able to do it a different way, or might be able to do things that E cannot.
The other thing to teach her is that we can notice things and not have to comment on them.
There's a simple technique (but not yet good for your daughter) about deciding whether to say something: T.H.I.N.K. This is a mnemonic for the following:
T - Is it true?
H - is it helpful?
I - is it inspiring?
N - is it necessary?
K - is it kind?
You might pick a few of those - maybe N and K, or whichever you feel are best - and concentrate on those. Also be aware of whether there's a lot of correction (or excessive praise for being correct) in your house or in other settings, whether it's your daughter doing it, or someone doing it do her after she either gets something right or makes a mistake. It can be very subtle, but even sometimes when we praise our kids for knowing something, we can inadvertently influence them to correct others.