"Too many attempts. Please try later." message on first Dropbox login after install
It appears that the current version of the app is buggy.  Nothing we can do about that.

However, a workaround was posted:


  I navigated into the website login > account > security > two-step verification. Added my phone number as my 2nd step of verification (they send a code for new logins) and low and behold I got into the app first try with no problems!


Using an older version of DropBox might also work.  I'd suggest 5.2.6, from February before the issue appeared.