It would help to know where you are in the game. Also, levels and maybe natures could help.
I never liked Air Cutter anyway and it's annoying in double battles since it hits both targets. I prefer Aerial Ace over it, since it's a guaranteed hit and more power, along with priority. Also, try Steel Wing. It's a pretty good move, especially for fighting Glacia's Glalie.
Grumpig needs some other move. Against a Dark-type (don't forget the numerous amount of Mightyena/Poochyena running around), you'll be forced to switch. I try not to switch in-game. It makes it speedy for the game. But, you could just be prepared in advance and it doesn't matter anyway.
Remember to teach Minun Thunderbolt or Thunder so that it has a better move to attack with.
Honestly, I've never used a Nosepass. I just hate slow Pokemon that are basically all defense. Blah. You could teach it Earthquake or something. Or level it to learn Zap Cannon, but it won't be much use for the E4. If you want to use it, go for it. It just needs some tweak in moveset but that's about it.
I'm guessing Skitty will evolve into Delcatty, so it should be fine. I can't really put much of an opinion on it anyway.
Azumarill doesn't really need Bubblebeam since it already has Surf. Definitely put Ice Beam on it instead. Other than that, it's set.
Yeah, I can't say too much. It's a bit limited since everything is based on movesets and that's it. You're looking fine anyway.