Jane's constant criticism. Any ambiguity?

Jane's constant criticism.

Does it mean a sentence "Jane has constant critism. " or a phrase with possessive case of Jane ending with "s"?

Usually, "has" can only contract to 's when it's used as an auxiliary verb. In your sentence it would be the main verb, so the 's is very probably possessive.

One sometimes encounters phrases such as "I've no complaints", which clearly means "I have no complaints", but I think this usage is mostly restricted to British English (and perhaps other dialects outside North America). I also doubt it occurs very often with "has", usually just with "have".

- Kef