Here is a list of contractions (and one Arabic word) from thefreedictionary.com which require an apostrophe at the start to indicate the omission of a character (or a breathing). Word and InDesign will incorrectly set these as opening quote marks unless you run a check for them. I show a sample InDesign grep query at the end of this post which you can customize for your text. Note that you will have to indicate both lower-case and capitalized variants – and that, for example, you might want to automatically correct 'em but manually check 'Em just in case it is a familiar form of Emily rather than a contraction of Them.
'em
'gainst
'hood
'Id al-Fitr
'll
'm
'mongst
'n'
'Neath
'pon
're
's
's Gravenhage
's Hertogenbosch
'sblood
'Sdeath
'shun
'Snails
'Swounds
't
'T is
'T was
'tain't
'tis
'tude
'twas
'tween
'tween deck
'tween decks
'twere
'twill
'twixt
'Twixt-brain
'twould
'un
've
Find: ('|‘)(?=(tain’t|Tain’t|tis|Tis|twas|Twas|twere|Twere|em|er)\b)
Replace: ’
