I've synced up my dropbox account and it's not asking me to "Enter the Master Password for your 1Password Vault" The keyboard pops up, but there's no box for me to enter any information. I've tried resetting the app, and the same issue appears.
I have the same issue on one of my test devices, a no-name Chinese phone with a 3.5" display. It's below the system requirements (it says 4.3" or more in the requirements) so I didn't bother to open a topic.
Do you know which device and which Android version you are using? You can get this information by going to Settings -> About phone/tablet (bottom of the list) and look at "Model number" for the device name and "Android version" for the version of Android.
I would be happy to look into this further for you. Could you tell me which device and OS version you are using?
I'm using a HP Touchpad with 10.1 cyanogenmod android 4.2.2
Unfortunately, I can only approximate your particular combination of device and OS. In my tests, I did notice some small rendering issues, but nothing that would account for what you are seeing. Do you have your screen locked in landscape orientation by any chance? There is a known issue with this during setup.