Everyone that has downloaded Omen 2 has noticed that there are some... issues. The author is aware of most of these, so fixes are on the way, but there's only so many hours in a day. Bugs and issues can crop up in strange places though, so it never hurts to report them. There are some minor things you can do yourself to make sure things work smoothly and be confident the problem isn't on your end, so take a look behind the jump for some tips.
First off, if you're having any issues at all and didn't do this before upgrading to Omen 2, my recommendation is to log off of WoW, go into your Addons folder, and delete the Omen folder entirely. This will be sure that no old files remain in the Omen folder from Omen 1.0. Some things, like the threat library Threat-1.0 are obsolete in patch 2.4. This may not have been removed in your original update, and has been reported to cause issues with Omen 2.0. Just wipe out the folder for now.
To simplify: Threat-1.0 is bad. Threat-2.0 is good. If you have Threat-1.0, kill it with fire.
Next, download Omen if you had to clean out the Omen folder. If you didn't need to clear out that folder, check your version by looking at the upper right hand corner of the Omen box. You automatically get notifications if your version is outdated when someone in your guild or raid has a newer version, but if you're checking on this prior to a raid, you can just compare it to the latest posting on WoW Ace. Make sure you have the most recent version each time you encounter a bug, because there's a possibility that has already been fixed in an update. The author has been working day and night to solve everything he can.
The most crippling bug that has been in Omen 2.0 so far is the immense CPU usage by the AOE and Healer Modes. This has been fixed, and you shouldn't need to worry about that issue anymore. It has been throttled properly now, so no more lockups or crashes. If you still see this issue, report it!
Many of the intended features for the UI have not yet made it into Omen 2.0, but rest assured that many of them are still on the way. It can't hurt to submit suggestions to the author, but many of the old features that we've grown to love simply haven't been implemented yet, though the intent is there. Patience is a virtue.
It may be frustrating to bump into so many bugs, but remain vigilant. If at all possible, do not become frustrated. Document what went wrong, write down any errors, and report them to the author. You can either do so over at WoWAce, or leave them right here for me at WoW Insider in a comment to this post, and they'll be passed along.
Keep in mind that all mods run into bugs, especially when they've just been built from the ground up. Omen and its predecessors had extensive testing on the Live servers before they were put out to the public. Omen 2.0(and Threat-2.0) was built from the ground up and wasn't able to have as much development time or play testing, as it was limited to the Fury of the Sunwell PTR and the content being explored on the PTR. The playtesting we, as a community, are currently doing with the mod will insure bugs are found and solved quickly and easily. Though it's a bit of a pain now, it's all going toward making Omen 2.0 better than it ever was.
Follow the few simple steps above, update Omen 2.0 often, document what goes wrong, and come on back to report it. You'll run into some hitches, but keep at it. Things will settle down, it may just need more than the two days it has had so far.
Oh, right! If you don't like the sound that comes with the threat warning, you can turn that off. Open the Omen configuration menu(click the wrench), go to Modules, then Single Target, then Warnings. Voila!