Sometimes, an error of 10 minutes may not have a major impact on the horoscope, but sometimes even an error of 3 minutes can change the chart a lot. It all depends on the individual case.
I use several dasa (periodicity) systems. One of them is Kalachakra dasa (periods of the wheel of time/destiny) of Sage Parasara. An error of 5 min in birthtime can cause an error of 1.5 years in the periods in this system!
However, there were occasions when I could cope with an error of 30 min!! A Chinese friend knew his birthtime with 30 min precision and, comparing his known past with astrological indications arrived at using various birthtimes, I could fix his birthtime. I could make several precise readings from that chart. For example, I asked him if his elder brother had a child in late 1989 or early 1990. He told me his elder brother indeed had a child in Feb 1990. I asked him if his elder brother had some failure in love, love problems and resultant emotional and health problems during late 1984 and early 1985. He told me his elder brother's girlfriend whom he had been dating for 4 years died in Jan 1985 and his brother was highly depressed. These predictions (readings) couldn't have been made unless I had an accurate horoscope. So I succeeded in converting a 30-min error window into a 1/2-min error window!
It's not always possible though.