I see the same issue with 1.4.1.

Still there in 1.6.2. Simple test case:

The next stable release of Debian is `buster'

hunspell will identify buster' (with the quote)

This sounds related: en-wl/wordlist#122

Related to #504

Same issue nearly 4 years later.
According to the ChangeLog

luism@lmm-notebook:~/project/hunspell/tests$ ./test.sh apostrophe.dic
=============================================
Fail in apostrophe.good. Good words recognised as wrong:
'is'

I wish I knew enough to PR a fix.

This seems to happens for Italian as well:

In Della morte dell'amore, from the tokenizer dell will be considered as wrong with suggestions ["del","della","dello","delle","del l"], where the output for dell' (note the straight apostrophe) is

{ index: 0,
  word: 'dell\'',
  stems: [],
  suggestion: [ 'della', 'dello', 'delle' ],
  correct: false }

Is this the root of this problem:

~$ echo "And no, spellchecking doesn’t work well in vim, because exactly this sentence is marked as misspelled." | hunspell -d en_US --check-apostrophe -l
doesn
~$

Hmm, with en_GB it seems to work, so I guess it is dictionary dependent.

This issue is still present in Hunspell 1.7.0, and includes the en_GB dictionary:

$ echo "He asked, 'Why can't I quote?'" | hunspell -d en_GB
Hunspell 1.7.0
*
*
& 'Why 1 10: why
*
*
*
& ' 15 29: e, s, i, a, n, r, t, o, l, c, d, u, g, m, f

This is an issue with the dictionaries. The English hunspell dicts from https://sourceforge.net/projects/wordlist/files/speller/ contain this line in their aff files:

WORDCHARS 0123456789

but this must include the ' character like this:

WORDCHARS 0123456789'

in order to detect contractions like "doesn't" as a single word.

If I manually modify change the dict accordingly, it works as expected.