The degree symbol is used for angles and arcs, temperatures, and the ‘proof’ of alcohol, among other things. You’ll even find it in harmonics. It started as a raised glyph of the digit 0, but best practice in typesetting and design now is to use a true degree symbol designed for the purpose.
The degree symbol is preferred because many fonts style the alternatives in ways that make them look very out of place as a degree symbol.
Font geeks love to debate readability and myriad other details about fonts. The other thing that matters when editing is being able to tell when the wrong character has been used. Font choice can cleverly conceal a wrong character hiding in a document: a 1 looks like an l, a superscript o looks like a °, an ‘ masquerades as a ′…
Changing the font to one that shows a more drastic difference between characters is one solution. Some editors prefer to edit in Helvetica, Calibri, or Verdana for just such a reason. If you modify the font of the “Normal” Style, it’s easy to undo this font change before finalizing the file. The client will never know the trick that helped you spot those apostrophes that should be primes. Just turn off Track Changes when you change the font.