Con Ed tested my boiler when I moved in and they said it was seventy
something percent efficient and that it wasn't economically
justifiable to replace it. I don't remember the exact number but I
think it was toward the high seventies...

It has a pilot. I don't know what an exhaust damper is, but if it's
something that closes the vent when the boiler's not running that's
tough because it shares the exhaust pipe with the water heater, and
anyway I don't really care how cold the basement gets.

I can't imagine how a boiler could be 98% efficient-- that'd mean that
only 2% of the heat is escaping through the exhaust...

In any case the boiler works and my gas bills aren't that high
(especially now that energy is cheap again).