Yeah, that's the trick. Almost all briskets taper off to a thin edge on one end. Often it's tough to find one that doesn't. Many bbq joints (including our friend, Jeff's Texas Style in Marysville) trim those thin edges off first to keep a more even thickness. The trimmings can go into hamburger, chili, or whatever.
As to slicing it, after smoking it can be hard to see which way the grain is running. Insert a toothpick close to the top surface while raw, running parallel with the grain. That way when it's done, you will still be able to tell the direction of the grain, and slice accordingly.
