I recently received a mail from a site visitor, who had discovered from Boswell's original birth certificate that he was actually born on October 18, 1740 and not on October 29, 1740 as is generally thought. There is, however, a perfectly good explanation for this apparent discrepancy.
When Boswell was born in 1740, the United Kingdom was one of a few European countries still using the so-called Julian calendar. Together with the rest of the U.K., Scotland switched over to use the Gregorian calendar in 1752. The two calendars are almost identical, with one important difference. In the Julian calendar every fourth year is a leap year, no exceptions. Over the course of time, however, this is not entirely in-sync with the length of the actual solar year. To compensate, the Gregorian calendar, introduced by Pope Gregory XIII in 1582, also has leap years, but three less over the course of 400 years. This is accomplished by excepting years divisible by 100 from being leap years - except for those divisible by 400, which are still leap years. The effect of this is, that for each century (except for those divisible with 400), the Julian calendar will get one day behind the Gregorian one.
The actual change-over in the U.K. took place on the day following September 2, 1752 - which was September 14 instead of September 3. The year 1753 was the first to fully follow the Gregorian calendar.
For Boswell this meant that while his birthday was on October 18, 1740 according to the Julian calendar, it was 11 days later - on October 29, 1740 - according to the Gregorian calendar. This is sometimes marked as October 18 (O.S.), October 29 (N.S.) for Old Style (Julian) and New Style (Gregorian) respectively.
It is therefore entirely correct when the original birth certificate states the birth of James Boswell as being October 18, 1740, which it was according to the Julian calendar then in use. And it is equally correct when modern sources states it as being October 29, 1740, which it is in accordance with the Gregorian calendar now in use.
As a PS it should be mentioned that the question of calendars has no major relevance to Boswell's personal papers and journals, as these were of course, with the possible exception of a few letters, entirely written after 1752.
There are a few references to the matter in The Life of Samuel Johnson, LL.D. where it is written for the year 1752 that "on the 17th of March, O.S., [Johnson's] wife died." Slightly further on Boswell quotes from the first entry of Johnson's diary for the year 1753: "Jan. 1, 1753, N.S. which I shall use for the future."