It's one of those things where lots of people will probably say "yes, I'd keep it if I found it in change", simply because neither $2 notes nor red-seal notes are everyday sightings, but it's still not actually worth anything above face value. Especially with the frayed edges and missing corners.
Trivia time: the "missing corners" may actually be deliberate damage. Back when $2 notes were more commonly seen, a superstition arose that receiving a $2 note was bad luck, and to make the bad luck go away you had to tear a corner off. I believe one of the main reasons why they stopped issuing $2 notes in quantity was that they were (comparatively) too expensive to produce; they had to keep printing replacements for otherwise perfectly usable notes with torn-off corners.
Trivia time: the "missing corners" may actually be deliberate damage. Back when $2 notes were more commonly seen, a superstition arose that receiving a $2 note was bad luck, and to make the bad luck go away you had to tear a corner off. I believe one of the main reasons why they stopped issuing $2 notes in quantity was that they were (comparatively) too expensive to produce; they had to keep printing replacements for otherwise perfectly usable notes with torn-off corners.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis