Our version of React Native is quite far behind which makes using libraries not already in the project difficult: you have to track back through versions to find a compatible version, which then may not be doing what you want since it's an older version.
We're also having trouble upgrading the version of React Native due to versions having breaking changes. I know it's technically still not v1.0, but in reality a lot of companies are using it so having a stable version would be nice. Since it's unstable, many libraries haven't updated to compensate so you run into the same problem as above, tracking down precise versions of dependencies which also still do what you want.
The build process feels pretty rickety and seems to rely on a lot of global state - I spent a while checking how we could update dependencies, but when I rolled back to a stable version I was unable to build even after re-installing node modules etc. I was only able to fix it after opening Xcode, removing all pod libraries and re-adding them; I have no idea why that worked, and there are very few clues on Github or Stack Overflow as to what specific errors mean. Fixing my build step took the best part of a day.
Overall, for a small app like ours, we're just spending far too long on non-development overhead, like fixing build systems or checking dependency versions, and will probably move to native versions at some point in the future. It may be a pain maintaining two separate versions, but we'll have solid integrations with payment gateways and lots of documentation and info on Github/SO for problems.
I like React and the idea of React Native, but at the moment it just feels far too unstable and unpolished to use. I'd like to use it in the future, but probably not until it's had a major version release.