John,
I have used corner chisels for years and am one of the "true believers" in them. That said, they are a pain in the seat cusion when it comes to keeping them tuned.
I think the "point" you find on a lot of corner chisels is the result of bad sharpening, often done on a bench grinder believe it or not. For that very reason, a lot of corner chisels are out there that have lost their temper at the cutting edge. Even if you sharpen it well, it may not keep an edge.
I start sharpening a used corner chisel by filing the edges square to the back. The best way is to stand the chisel straight up on a wide mill bastard and work it back and forth until it's trued up. At this point use a lapping stone to flatten the backs. Then use a file to re-establish the bevels. 25 degrees for softwood and 30 for green hardwood. You might consider going as steep as 35 for recycled oak or hickory. To keep the file from dinging up the bevel that you aren't trying to sharpen, make it "safe" by grinding off the serations on the edges. Always push the chisel from the socket end towards the cutting edge. Once the bevels are filed (use a finer file to finish) you will have a small wire edge on the bevels. DON'T break it off!
Lapping the bevels and honing the micro-bevel is a little harder to explain, but will be obvious as soon as you try it. Hold the chisel against the corner of your waterstone so that one bevel is laying flat agaisnt the stone on top and the other is draped over the side. You will need to swing the chisel out so that the bevel you aren't honing doesnt contact the side of the stone. Draw the chisel toward you reatedly until the wire edge starts to "loosen". Now rotate the chisel up 5 degrees so that only the cutting edge you want to hone is contacting the stone. Pull it towards you. Repeat as needed until the wire edge falls off and your micro bevel is honed. Now switch the chisel to the other edge of the stone and repeat.
Viola! You're ready to cut beautiful mortices.
Enjoy your sharpening experience and take your time!
Rudy