The + button to add new block works once, but does not work on subsequent button presses. This issue was discovered on the Android Emulator, and has not been reproduced on a real device (attempts were made, but the issue was not encountered).
Steps to reproduce:
+ button and choose new paragraph block+ button again and choose a new paragraph blockResult:
A new paragraph block is not created. The focus changes to an already existing block.
Screenshot:

After testing this issue further, I have discovered that the + button to create a new paragraph block fails when a Heading or Paragraph block is focused, but succeeds when a Page Break block or Code block is focused.
Also, it seems that using + to add either a Page Break block, or a Code block, succeeds, regardless of which block type had focus when tapping +.
Some other discoveries:
Some of these issues could be same / related to #196 or #311.
The recent upgrade (React Native to 0.59, React to 16.8.3) seems to have a source map issue, which has made it difficult to use the JS remote debugger. I am temporarily resorting to a bisection method to try to isolate the changeset that may have introduced this issue. I will test this issue manually using the following steps:
+ button and add a new Paragraph blockProgress:
I began this bisection manually, explicitly selecting release tags / versions to narrow the scope at that level of granularity. The results so far indicate that the regression was introduced somewhere between v1.1.0 and v1.1.1. I then proceeded manually, increasing the granularity to mostly PR merges, at first in timestamp order, then by transitioning to topological ordering.
I encountered a few commits (as expected) that either did not build, or began with a red screen at startup, because the process is agnostic to whether or not a commit represents work in an "unfinished" state.
I went a little bit further with git bisect. Several commits near the condition boundary result in a failed build, so progress has slowed. Attached below is the log from git bisect.
From a coarse view, this issue appears to have been introduced during the upgrade to RN 0.59, but I have not pinpointed the exact commit.
Most helpful comment
Fixed in https://github.com/wordpress-mobile/gutenberg-mobile/pull/857