It's not an uncertainty, it's a different calendar system. 16 Feb 1723/24 means 1724 by the calendar year starting Jan 1 (New Style, NS) and 1723 by the calendar year starting Mar 25 (Old Style, OS).
The wikitree policy is to use the NS form, 16 Feb 1724.
For the usual convention in British history, what you do is take the original date, and if it's before 1752 and on or after Jan 1 but before Mar 25, you change the year to the next year, so if you see 16 Feb 1723, that should become 16 Feb 1724. If the date is in or after 1752 AND it uses the slash convention, use the latter date. If the date is recorded in or after 1752 and it doesn't have a slash, don't change it because it should be in the modern format already (unless there's some internal evidence that the clerk was still using the old system). However, I highly recommend stating in the biography whether it's an OS or NS year or using the slash notation, just because it's hard to be sure that everyone's on the same page with this.
Note that this ignores the Julian/Gregorian conversion. 16 Feb 1723 OS is really 27 Feb 1724 NS, but the usual (but not universal) convention is to ignore that 11-ish day difference and just signify the modern year while retaining the original month-day. You just have to remember that if you're calculating date differences, you may have to look at the Julian/Gregorian conversion as well.