MedBetterDNA 5.1 extension for the Chrome browser adds a new option called "show full length Notes". This option displays up to 99 lines of entry notes on the DNA results summary, rather than the AncestryDNA default of 2 lines.
Why limit it to 99 lines? Because when I set the extension to allow any number of lines, the browser ignored it. (Browser internals can occasionally misbehave.) Regardless, 99 lines seems like enough for almost any useful purpose, but if I'm wrong, someone should let me know, and probably will.