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Is there a delay before coordinates are actually updated ?

No, but you may have to reload the page to get the new coordinates. I doubt it, though.

I noticed you had 48.0 for the latitude. I got out an atlas and looked up Paris. It appears to lie almost completely within the range (48 deg, 40 min) and (49 deg) north latitude. I altered your latitude to put you at (48 deg, 50 min). You now look like you're in Paris relative to the river Google is showing.

I've had some questions from other people about map accuracy. So far, it's just been that we're not giving enough digits after the decimal point. One minute of degree at the equator is (very roughly) 1.16 miles. One minute of degree is just 0.0167 of a degree. That means if you enter 48.0 instead of 48.8333, you're off .8333 / 0.0167 = 50 minutes or (roughly) 50 miles.