So what does it mean if my old brake pads wore in a tapered fashion? Haven't taken them off the bike, but the outboard pad does look like it's worn in a wedge shape . . . ? Any big concern there?

 

without a photo, it sounds like you are describing a situation where the pad is hanging up on the pin or something at the top and the bottom is wearing faster than the top...depending on the taper direction, it could be a piston sicking and you are wearing more on one side of the pad than the other...can you snap a photo?

 

Not so much a "concern" but something to be aware of. It can even be caused by caliper mounting alignment or as stated above (i.e.. hanging up somewhere.)

Always a good idea to take a flashlight and inspect your brake pad material thickness as part of your T-CLOCS inspection during pre flight.

Here's an example of someone whom wasn't paying attention...(ahem!)