Advanced caching options are not supported for the build-in maps application. If other applications would provide this using Google's maps data, they would act against the Google Maps TOS. See section 10.1.3 "Restrictions against Data Export or Copying" - (b) "No Pre-Fetching, Caching, or Storage of Content".

This leaves us with apps which use other maps data. Such as...

OffMaps 2 (for iPhone/iPad)

OffMaps 2 allows you to download maps for offline use. The maps data is originally retrieved from OpenStreetMap.

• You download maps on a per-region-basis. Two maps are included for free.
• You can purchase a download 'licence' for unlimited maps for $5.99.

I wondered myself how they could demand money for open data - they say:

We do not charge for the data, but for the service we provide around it. We clean the data and leverage its full potential from removing unneeded information via linked addresses with streets to providing a public transport layer. We also need money to feed the hamsters in our server farm treadmills.

I believe it's related to the accuracy of the compass. In my experience, the compass is quite inaccurate and maps do not align perfectly with real life, but usually the actual alignment is somewhere in the cone (I say usually because sometimes they're so inaccurate that it's outside even that, especially when I'm inside a big metal car). This is similar to the blue circle around the dot that represents uncertainty in your location.

It probably changes its acuteness because the compass becomes more and less accurate over time. The angle of the device may have something to do with this (based on the built-in compass app and personal experience, the compass seems to be more accurate when the device is laid down flat).