There is a concept of Mekach Toyus (mistake-based deal) in a marriage. What would be considered Mekach Toyus? Suppose when the bride or groom figured out that this was a Mekach Toyus and remained together for a while longer can they still say Mekach Toyus?
See this lecture (mp3) by Rabbi Michael Broyde.
If there is a significant problem of which the other party was unaware, and it is the type of problem that the average reasonable person would absolutely not be willing to live with, then the marriage was effected on faulty conditions, and is automatically dissolved.
If I recall correctly from Rabbi Broyde, the Chazon Ish in Israel said such a case could exist, but he couldn't think of any. Rabbi Moshe Feinstein in fact ruled on several such cases, such as the bride who suddenly finds out that her husband:
- Converted to Christianity a long time ago and has since been an avid churchgoer.
- Has been in physical relationships with several men before and throughout their engagement.
- Has previously been institutionalized on multiple occasions for severe psychosis, and is currently back in an institution.
(Those are three separate cases. Not one combination, oy!)
If, after learning of the problem, the couple chose to stay together (especially if they had marital relations), the concept becomes much less clear, as that could be a new act of marriage demonstrating that the newly-discovered fault is really not a problem for them. Rabbi Broyde mentions the complicated case of a woman who discovered something egregiously wrong with her husband, but chose to stick around for a few more months until she had enough evidence to take to a divorce lawyer; her staying around was not a demonstration of acceptance.
Tosafot in Kiddushin 9A discusses not using a diamond ring for Kiddushin. Since if the woman will think the gem is worth more than it actually is, this would be a Mekach Ta'us.
There are, however, major commentators who say the Kiddushin is still valid, and some that disagree, see here (discussing a fake gold ring).
Here is a blog post that links to a discussion regarding Rashi, Tosfot, Maharam, and R' Moshe regarding what is considered a Mekach Ta'us with regards to Kiddushin.
Also, here is a 6 part shiur from BusinessHalacha.com on the laws of Mekach Ta'us that may cover some of these issues.