While writing, I usually read aloud the text: I like that what I write be not very different from what I would say. Since paragraphs are separated by pauses, which are usually quite obvious when talking, a bad paragraph break or a missing one tends to make itself quite obvious in this way.

This does not constitute a rule, of course, for paragraph breaking, but is a useful way to probe them. 

Good paragraph breaking is like pornography, in a way.

*Regarding your specific example:* without context, I don't think you we can decide if a «It remains only to show some big thing» is better at the end of a paragraph or at the beginning. If you have a paragraph whose point is to explain *why* such to obtain the desired result A it is enough to prove B, then it may well end with a «It remains only to show that B holds.» On the other hand, if that point was done earlier in the argument, and since then time has been spent on doing some other menial task, it would be nice to start the paragraph that begins the remaining task with an annoucement that «It remains only to show that B holds» if only to be nice to the reader who might have by now forgotten the big lines of our reasoning.