Which punctuation to use in "I wonder _ could there be..."

Solution 1:

It should be:

• I wonder if there could be more precise translations. . . .

However, if you must break that, you can use a comma, colon, or em dash:

• I wonder, could there be more precise translations. . . ?
• I wonder: could there be more precise translations. . . ?
• I wonder — could there be more precise translations. . . ?

Note that:

• could and there are transposed in the first case;
• it is an em dash — not the underscore character you used;
• the question mark at the end is needed in the second set.

Solution 2:

You've also got the option of using a period and writing two sentences, which may the best choice because the first two words signal a declarative and not an interrogative:

I wonder. Could there be more precise translations ...?

Both a colon and a semicolon can be replaced by a period (end stop). A period seems better than any other type of punctuation to me, although an em-dash would be fine for dialog. The question mark has to be there because subject-verb inversion signals a question. Dialog writing isn't bound by any set of strict punctuation rules. All that's necessary is that the writing communicate what you want it to communicate. Colons and semicolons are very formal. Commas and em-dashes are informal. I don't like the comma version:

I wonder, could there be more precise translations ...?

because the reader will start out using declarative intonation and have to switch to interrogative intonation. For me, that means two sentences. But YMMV, as people are constantly saying.

Solution 3:

If it's an informal setting, the dash is appropriate:

I wonder — Could there be more precise translations ...?

I don't suggest using a this construct in a truly formal context. If you choose to do so, a period seems to be the best choice:

I wonder. Could there be more precise translations ...?

The best option would be to rephrase based on what you really want to emphasize with the sentence. In the given context, the act of wondering isn't the important idea here. If you want to draw attention to the act of wondering, then I suggest a preceding sentence with a little more meaning.

Solution 4:

I’m not sure what you mean by 'obviously the of doesn't belong'. If you mean if, it certainly does belong, but it needs to be followed by there could, not could there. The second sentence would indeed occur in speech, but it would be out of place in formal writing. If you write it in something like an email to a friend, or in a Facebook post, the punctuation you choose isn’t hugely important. A comma after wonder might be enough, with a question mark at the end:

I wonder, could there be more precise translations?

Solution 5:

I'd use a comma, a colon or an ellipsis, depending on the impression you want to create — ellipsis is thoughtful and undecided, comma for neutral, colon gives it a strong, decisive feel.