These are a few things I (and a few others on the internet) have noticed.
Shinji and Misato's conversation in the car is completely different than the one in the series. It shows how Shinji is more cynical than he was in the TV series.
Misato revealing Lilith as Lilith so soon means that Misato knows everything about Second Impact from the beginning, unlike in the series. This can be attributed by her higher rank of Lieutenant Colonel in the movies.
The angels dissolve once they are defeated which makes things at a little tricky. The angel with energy whips that Shinji stabbed to death, Shamsel, was the angel from which Nerv got a core sample. That core sample was used to make a S2 engine prototype for Eva Unit 04. Without that sample, Eva Unit 04 would not disappear with the Nerv 2nd Branch in the US. However, it still disappears in Rebuild 2.0 if the preview at the end of Rebuild 1.0 is true.
When the first angel in the series, Sachiel, is healing itself from the N2 mine explosion, Gendo and Fuyutsuki mention that the angels have the Fruit of Life and humans have the Fruit of Wisdom. This is not explicitly said in the series. It's hinted in some parts of the series and only said explicitly in End of Evangelion.
There is a mysterious chalk outline seen in the first few minutes of Rebuild 1.0. No one talks about it or hints anything about it in the movie. Some people believe that it is an outline of a petrified Mass Production Eva left over from Third Impact as "proof" that Rebuild of Evangelion is a sequel to the TV series and End of Evangelion. I am not one of those people.
Seele and Gendo speak of the Human Instrumentality Project as their "Covenant with Lilith." It can be a new, twisted way in seeing Instrumentality as a religious rite as that is how Seele rolls.
There are nine coffins on the Moon when Kaworu emerges. Four to the left of Kaworu are opened, Kaworu was in the fifth coffin, and the other four to Kaworu's right are still closed. There could be multiple Kaworu bodies in the coffins, but the biggest thing about this is Kaworu seems knowledgeable of the current events. What does this mean? I have no idea.
Another thing on the Moon with Kaworu is an excavation site with an unarmored Eva. An Eva was found on the Moon. Something is not right with that sentence. Rebuild 2.0 may have a better explanation since it seems to go over Second Impact.