Thank you for your post.
I am unable to replicate the problem with FileMaker Go 11. After I tap a Pop-Up menu field, I tap "Other...", and I'm able to enter any value, tap Save, and the value is then displayed in the field. I can then switch to another record.
Do you get a hang? Or, does FileMaker Go 11 quit? If you create a new field with the same value list and access it remotely or locally with FileMaker Go 11, do you still get the same issue?
Any other information you can provide may be helpful in narrowing down the underlying cause.