The iPhone and iPad do a lot of things well, but if you agree that the built-in microphone could use some improvement, you should check out the Mikey Digital add-on from Blue Microphones.
Blue is known for the very high quality microphones for Mac and other uses, so it's nice to see them bring their expertise to the iOS world.
UPDATE: You can get a GREAT deal on the Mikey for just $12, using the coupon code PODC15 at http://www.buydig.com/shop/product.aspx?sku=BLM4920MKYR&omid=200&ref=cj
Now, before you pooh pooh the Mikey because it uses the 30 pin port, consider the following. First, there is an integrated USB charging port, so even though you're using the 30 pin port, you can still charge your iOS device using USB. Second, the Apple 30 pin to Lightning adapter works, so you can use the Mikey with more modern devices. Of course, you can use the Mikey with older 30 pin iOS devices and it makes a great, low-cost recording solution for classes, conference rooms, etc. You can use your favorite app, or Apple's built-in one, to record audio notes, but now you'll do so with superior quality.
Blue makes their own app, called Blue FIRe, or they recommend a variety of higher end recording apps that work with the Mikey Digital.
I let a videographer friend of mine try out the Mikey and put it through its paces. She liked the build-quality (the grill is a nice protective metal) and the multiple ratcheting positions. This lets you get a good view of the app/screen while positioning the Mikey where needed for best audio pickup. You can record just about anything... lectures, interviews, voice memos, etc., and then transfer them to another app or computer for further editing or use.
Here are the specs for the Mikey Second Generation Microphone