Eddie Thawne shot and killed himself in order to save Barry Allen from being killed by Reverse Flash. That essentially erased Eobard Thawne from existence.
Realistically, that should have reset the entire timeline. So then we'd have the following:
1. Since Reverse Flash doesn't exist anymore, the real Harrison Wells was never killed by Eobard Thawne, so he should still be alive. THat also means S.T.A.R. Labs is still years away from becoming a success (which is true because this was talked about in season 1). That also means, Barry Allen wouldn't be the Flash (not yet anyway).
2. Nora Allen is still alive and Henry Allen never goes to prison.
3. Barry Allen "possibly" never becomes a Forensic Scientist for the Police Department.
4. Barry Allen never moves in with Joe West.
5. Barry Allen still becomes the Flash but not for another 5 or 6 years (as revealed in dialogue from the first season).
6. Dr. Wells fired Pied Piper (can't remember his real name) because he had moral issues with the particle accelerator. So in a reset timeline, Pied Piper could still be working at S.T.A.R. Labs.
7. Ronnie would be married to Caitlin Snow since he didn't become Firestorm (but most likely would later on down the road in a reset timeline).
The list goes on, but I can't think of anything more. So, realistically, what happened in the season 1 finale should have reset the entire timeline. Season 2 SHOULD have realistically opened with at least a five year time jump where the above list applies. And then we'd have to go through Barry Allen's journey to becoming Flash again...
But instead, the writers chose to keep the original timeline when anyone giving this serious thought, it doesn't make sense. I was worried the writers were going to make a mess of things by introducing the multiverse if not done right. But I was wrong...they already have made a mess of things.
And it's looking like the writers don't even care. They keep this up, the Flash will be cancelled before or during season 3. It's already too confusing and pretty messy.
But as Iron Man Unit and have both speculated, maybe Rip Hunter comes along and stops Eddie from killing himself, thus bringing back the Reverse Flash back into existing again.
WHo knows. I just hope the writers are aware of this mess on their hands and fix it before the show is cancelled.
The giant rift that opened above the city was a result of the massive paradox that occurred as a result of Eddie killing himself. Closing it effectively prevented the paradox from wiping out their timeline but caused the breaches into Earth 2. So it's basically been explained already and is in fact the cause of the season 2 problem.
Honestly, though, it's not a big deal. Technically the same argument could be applied to season 1. Eobard's actions in the past should realistically have resulted in such a drastic change to the future that he would have immediately been wiped out of existence. The dozens of other major events he changed probably would have resulted in the same thing. I doubt the show will get cancelled as a result of this. Frankly it would be more confusing if they tried to explain why things stayed the same rather than just glossing over it.