I'm an infrequent user of the Google Maps app for iOS (the downloadable turn-by-turn app from Google, not the original Google Maps app written by Apple), typically using any number of standalone GPS navigation devices or the community-driven Waze app.
So when I fired up the app today and attempted to navigate to a regular destination just two miles away (to see if Google would eventually try to anticipate this destination in the Google Search app for iOS (which incorporates Google Now technology not otherwise available on iOS), it was more than a little disappointing that the app estimated that the trip would take 24 minutes, covering 13 miles. Even though the app displayed my requested destination and point of origin (my Current Location), the route originated several miles away. Switching between Automobile, Public Transit, Bicycle and Pedestrian modes did not help - each still attempted to start my trip miles from my actual location.
Changing destinations - even navigating to a point a few feet away - made no difference. Quitting and restarting the app and the phone made no difference. Other navigation apps worked correctly.
What finally worked was uninstalling the app and downloading it again from the App Store. It was NOT the same version as I'd originally had (updating to v220.127.116.1121), so the version change may or may not have played a part.
Researching this yielded few helpful comments, but did reveal that many Android users have experienced similar symptoms.