Yup, the Simplify function is always what I end with. I also occasionally run it a few times during the cut line creation too.
Hard to describe my process, but for anything that's on a solid background I will usually start in Photoshop and use the magic wand to select the background, then invert the selection and fill with black. I slightly blur this and save as a separate file the exact same dimensions of the main artwork. This basically gives the the shadow of the artwork. Then it's into Illustrator to live trace, pathfinder/unite, and stroke with rounded corners.
The "trick" that I do for repeatable results and to avoid ever having sharp corners is to create the first stroke a little larger than what I what the final border to be, and then expand that and delete the inner side, then use the outer edge to do another stroke with curved corners that basically goes back inward. Then expand, delete the outer edge, simplify, blah blah. It can be very hard to describe but combined with simplify it is capable of doing a slightly less "computer generated" look than just the one-time outline/expand look that is too perfectly bubbly. My simplify settings are usually 98/165 and I always preview to see how many points I'm cutting.
PM me if you need a more in-depth description of that process. I realize it probably reads like nonsense. And again, I use his primarily for small graphic stickers that are being 100% die-cut, but it applies to any kiss-cuts I do as well.
Other than that I think you know instinctively what to avoid as far as cutting to far into a design(concave) or having thin delicate areas.