Is the sentence "What to do?" very old fashioned idiomatic English, or is it simply ungrammatical?

On a foreign-language-learning forum there is a question that's given the English translation "What to do?"

My impression is that that's an example of very old fashioned English. Maybe something I'd expect in Shakespeare or at least a snooty upper class character in an old black-and-white movie.

Or am I mistaken and it's just a simple bad translation into an ungrammatical sentence lacking a main verb?

References:

• A Spanish-English forum thread on Duolingo about "What to do" in which some native English speakers take issue with it.
• (I'm still looking for the original Duolingo thread which inspired me to ask this question, which was in a Chinese-English forum there...)

At Mari-Lou's suggestion, here are some of the comments against. There are also comments for, which I'm not listing. You can scan through the thread if interested:

• Not at all common without a subject. More common: What am I doing?
• It may be heard in the UK, but it is not common. In context, it would probably be understood. But from a native speaker, it would sound archaic and peculiar.
• Native speakers in the US never say this!
• I have never heard anyone say What to do? in English
• "What to do?" Makes no sense as an English sentence.
• This is not a widely accepted way to express oneself in English.
• In English " To do what? or Do what! would be normal but not "What to do?" as a question is not correct in my opinion.
• I don't agree with Duolingo's translation on this one. In Spanish you can ask "Que hacer?", but in English "What to do?" is not a grammatically correct question.
• "What to do?" sounds like a mistake a Spanish-speaking person would make at an early stage of learning English.
• I certainly recognise what you say, but it doesn't sound like English as I speak it.
• Does any english speaker actually say "what to do?" I definitely don't

Solution 1:

It's at least idiomatic. It's also often rhetorical: "I was walking along and found a bag of money. What to do? I could call the police, but no one is around..."