We have over Christmas and would recommend it!
As you know from the website, Menehune Mischief happens on Sunday, Tuesday and Thursday evenings. Make reservations early because it does fill up! (We tried to get in the week of our visit, and it took two days of trying with Dining to get us a reservation.) The show may run from 5:15 PM to 6:00 PM, but you can get seating for the dinner and show as early as 4:30 PM. Dinner with Menehune Mischief costs a little more (Adults $49.00, Children 3-9 $24.00) than the regular price (Adults $47.00, Children $21.00), but you get the extra experience and I'd say it's worth it.
When you arrive, you are greeted by Donald Duck in an Aloha shirt and straw hat, with whom you can take pictures. A photographer will take pictures that a cast member will later bring around to show you on an iPad with the option to purchase a package, but they'll also take pictures with your own phone or camera. The buffet line has the same offerings as dinner without the show. I don't think the regular dinner offers any characters. We had an early seating and got our food before the characters came out. With Menehune Mischief, you'll always see Stitch and we also got Goofy (although I've seen some pictures online with Chip and Dale). The two characters go table to table and interact with the guests. Because they're Disney's more silly or mischievous characters, the exchange is really fun and we felt like the characters spent a good amount of time playing and taking pictures at our table and every other. If a character missed your table, or anyone in your party missed the characters (because they were getting food or otherwise away), a cast member did come around to inquire if we met all the characters towards the end of our meal and presumably would've sent the characters our way if we missed them.
Later in the evening, Uncle comes out with a magical book and tells the story of the mischievous menehune. The restaurant can be pretty loud, so we had a hard time hearing what Uncle was saying, but hijinks ensue and Stitch and Goofy get in on the act. Much like the breakfast buffet with Aunty, Uncle calls on the keiki (children) to help and the characters lead the kids in a sort of conga-line around the restaurant. Our DD preferred to eat and didn't join in the fun, so I can't really write more about this. You can stay as long as you'd like. We have a toddler who is a difficult eater, but never felt any pressure to leave.