One of the biggest deal-breakers in the ceremony -- more than the language of the ketubah -- is if the witnesses were shabbat-observant. There are other issues in non-Orthodox ceremonies, but that's by far the biggest.
In theory the Talmud talks about situations where a couple would have in mind that if the wedding ceremony itself isn't valid, they would still want to be married vis-a-vis halacha; as we are all witnesses that they are living together as husband and wife, that could count. However it's not clear whether this applies to couples who aren't cognizant of traditional halacha.
Note that the penalty for adultery is far worse than that for premarital relations, so rabbis lose a lot more sleep about "maybe her divorce wasn't valid before she remarried" than "maybe this happily-married couple didn't have a valid marriage."
Hence if a baal teshuva couple tells their rabbi that they didn't have shabbat-observant witnesses, he may very well recommend (if it won't burn bridges) that they undergo an Orthodox wedding ceremony. I've seen one of these. They ask everyone to stay for after davening on Sunday morning so you have a minyan, it takes ten minutes. (And no you don't need a band, a caterer, photos, any of that.)
On the flipside, though, an Orthodox rabbi will play it safe and always ask that a divorcing Jewish couple go through an Orthodox divorce ceremony (a Get). It can't hurt.