- Being easily able to tell the difference between characters that are otherwise similar (such as O vs 0 and l vs 1 vs I)
- No ligatures and no kerning (a monospace font should not have these features)
(The two above are perhaps the most important (and I think are probably already common enough); the below are less important but still might be good to have)
- Bitmap font for on screen, and also scalable fonts suitable for printing
- Versions of fonts for different character sets (such as ASCII and APL and PC), without using Unicode or other unified character sets
- Possibly, glyphs for control characters (if it is PC character set then it already does, since they are graphic characters with the same codes as the ASCII control characters; another alternative if not the PC character set, is to use ISO 2047)
- Visible: tabs, trailing spaces, spaces that are mixed with tabs, line continuation, page breaks (this is more of a feature of the editor or display rather than of the font, although a font might include glyphs specific for this purpose with special character codes)