I purchased the application for my iPod almost as soon as it came out, and my wife bought a copy for her phone as well. We went for a trip to my Mom's (500k away) on the long weekend and found a few caches with it, and I thought I'd give some of my feedback here.
I was mainly looking at the app for a way to quickly see cache information to plan trips when my laptop wasn't available, and to make paperless caching a little easier. Currently I use my iPod for paperless caching by creating html files from my pocket queries using gpsbabel. I then copy these to my iPod and use AirSharing to browse them. While this works it is difficult to navigate, and air sharing is very slow to render pages.
I realize that there are other apps coming out that can handle large pocket queries, but they cannot access the GC.com site, so I figure that they will complement the geocaching.com app, not replace it. When I can use my laptop to plan a trip and create the GPX files that I will need that will be the way to go, but if I want to do some spontaneous caching the live access feature should be quite useful. Ideally I'd like to be able to plan out and save the caches for a small trip on my iPod since unlike the laptop I can pull it out anywhere and see what's nearby. The comments I'll be making about the app are in light of this kind usage.
First the good: I really liked the browsing interface - much nicer than browsing html files. It was very quick to access most of the information that I wanted.
One thing that was very frustrating on the iPod was that the app didn't remember my location. I would like to be able to set my location (either by entering co-ordinates or a waypoint code) and have the application remember it. This would make performing repeated searches much easier.
As others have mentioned I would like to be able to edit my previous search when returning to the home page. This would make it much easier to refine a search.
It would be very useful if the app downloaded addional waypoints (parking, trail head etc) for the cache.
Being able to sort the saved caches by distance from my 'current' location would make the saved cache list much easier to browse.
Having a 'nearby caches' button on each cache page would make it much easier to find different caches in an area. I was constantly finding the coordinates of a cache, and then going back to the main search page and using those as the root of another search in order to explore caches in an interesting area (this would be an issue on the iPhone as well as the iPod). Ideally the 'nearby' button would work with saved caches when offline. The nearby button could just save the cache location as the 'current' location and then jump to the search page to display nearby caches.
For iPod paperless caching a bulk save option would be really appreciated. Saving all caches in a list at once would make it much faster to prepare for a caching trip. (It would also help if there were a saved/not saved icon on the cache listing page).
Browsing for caches using a map is much easier. While a map of all caches on the device would probably be a tall order (but very useful) would it be possible to send the thumbnail map from GC.com? (and then store it on the device when the cache was saved?) For the iPod saving the satellite and terrain maps at high resolution along with the cache would be a very handy feature. This should be fairly easy since the map could be generated on the server.
On the whole I found the first experience slightly frustrating, but I think that it is possible to make a reasonable paperless caching and planning app for the iPod by adding a few features. The app is obviously designed to grab the nearest caches quickly which is really only possible on the Phone, but I hope that iPod development does continue because I do see potential there.