Tom Gewecke wrote:
Normally you would only use this when writing certain European languages
It's a very small point, but I'll take issue with that. It is also used in English, in certain specific circumstances.
For instance, if you happen to be in the book trade, or have some connection to books (especially rare ones), then you are familiar with terms like quarto (4º) or octavo (8º), and, of course, folio (2º). (The famous Gutenberg Bible was a 2º; and, if your language happens to be English, then the words "Shakespeare" and "folio" go together like a horse and carriage.) If you are a classical musician, then the indication "Tempo Iº" or "Tempo 1º" (tempo primo) is no novelty to you. Basically, you could come across it anywhere in English where words of Latin, Italian, or Iberian origin are used.
But isn't the distinction between the masculine ordinal indicator and the degree sign, the most trivial of trivia? Does it matter which one is used? Well, yes, it does.
One reason is outlined by Tom: the glyphs (the visual representation of the character) are actually different. The degree sign should be always round, a circle; while the other one is derived from the letter "o", so it should match it -- sometimes circular, but most often not; moreover, again as Tom points out, in some fonts it is underlined.
But there's another reason, and it has to do with how text is parsed. When we read, we can tell the difference between 1° (1 degree of angle) and 1º (primo) from the context. But that's because we're human beings, and we are (or, anyway, supposed to be) intelligent. Computers, however, are not intelligent. In fact, they're some of the dumbest machines ever invented. The reason why writing good software is such a difficult task is because software is a method of making dumb machines accomplish tasks which require intelligence. So, if you expect a computer to handle your text, to print it correctly, to index it, to search it, to use it in any number of ways that perhaps we haven't even thought of yet, then you have to tell it explicitly that it's either one or the other. And you do that by entering the correct character.