Using Foursquare means user-generated content. It is MUCH more accurate than Yelp and is always up to date because the users ensure it is.
Exactly. The biggest problem with Maps is not actually the maps themselves (the *streets* are in the right places, after all) but the terrible location search.
One of the reasons that the location search is bad is that it's not enough just to have a big database of locations. Even if Apple's database was comprehensive and up to date (which it isn't), you need to know how popular each place is. Not just to decide what locations to draw on the map, but also to form meaningful, relevant search results.
The same applies when searching for place names. You need a search engine that is smart enough to know that someone searching for "London" in Europe probably means London, UK and not London, Ontario. Likewise, someone is southwest Ontario doing the same search probably does actually mean the other London.
This is something Google understands. They also have a huge number of users and can form data on popularity based on the number of people searching for them. As a result, their location searches are very good.
Foursquare is also very good at doing this - the more check-ins a place has, the more likely it's something that users are actually searching for. Getting this user-curated, up to date data into Apple's Maps would be a big improvement indeed.
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Apple are still dependent on Google for Maps. They just have a lot less control over it now as they have nothing to do with the app, rather than something.
Apple didn't have a lot of control before, either. They were dependent on their agreement with Google as to what they were allowed to include in the maps app, and things like 3D vector maps, search suggestions/autocomplete, and turn-by-turn navigation weren't available.
The only reason Google Maps has turn-by-turn directions and 3D on iOS today is because Google had to put those features in to be competitive - you can thank Apple Maps for that