As stated in, When did single quotes in HTML become so popular? and Jquery embedded quote in attribute, the Wikipedia entry on HTML says the following:
The single-quote character ('), when used to quote an attribute value, must also be escaped as
'or'(should NOT be escaped as'except in XHTML documents) when it appears within the attribute value itself.
Why shouldn't ' be used? Also, is " safe to be used instead of "?
' is not part of the HTML standard.
" is, though, so is fine to use.
If you look at the list of HTML 4 character entities, ' isn't on it. That's why it shouldn't be used. From C.16. The Named Character Reference ':
The named character reference
'(the apostrophe, U+0027) was introduced in XML 1.0 but does not appear in HTML. Authors should therefore use'instead of'to work as expected in HTML 4 user agents.
Basically some browsers don't understand XML/XHTML so they rely on them falling back to trying to interpret it as HTML and ' is not a valid HTML symbol.
Edit: As noted in comments and the other answer, " is fine (see the list of references link above).