I've heard that Dan was born out of wedlock. Is this true? Could someone provide me with a source for this information?
To explain how Reuven didn't sin with Bilhah, he explains based on the gemarra in Yevamos that Avaraham's children couldn't marry a shifchah. Therefore, Yaakov freed Bilhah and Zilpah when he married them. The way he freed them was with biah, which simultaneously freed them and was mekadesh them. However, Reuven held that biah doesn't free a shifchah and therefore felt that his father was never married to her, since Kiddushin doesn't work with a shifchah1. This is why the children of Yaakov called the children of the shefachos slaves, since they follow the lineage of their slave mother. Therefore, according to Reuven, Dan was born out of wedlock (as well as Gad, Asher and Naftali).
1This is why Reuven moved Leah's bed and replaced Bilhah's. He felt Yaakov wasn't married to her, only Leah. Also according to his shita, in theory he could be with Bilhah, since she's not his father's wife. So the verse considers it as if he was with her. This also gives new meaning to what the gemarra says: כל האומר ראובן חטא אינו אלא טועה, whoever says Reuven sinned is mistaken. A new way to read it is: Whoever says Reuven sinned (is wrong since), Reuven made a mistake (in pesak). He held Bilhah wasn't married to Yaakov, but the verses tell us Yaakov was right.
You are probably thinking of the son of an Egyptian man and an Israelite woman, who cursed God's name (Leviticus 24:10). His mother was Shlomit the daughter of Divri from the tribe of Dan (24:11). Rashi describes her as a prostitute, implying that her son was born out of wedlock with the Egyptian man. Rashi further says that the tribe of Dan was specifically mentioned here to teach that a wicked person brings shame to his entire tribe.
As hazoriz notes in his answer, Dan the son of Jacob was not born out of wedlock.
From the simple reading of the Torah it seems that it was in wedlock
She said, “Here is my maid Bilhah. Consort with her, that she may bear on my knees and that through her I too may have children.” So she gave him her maidservant Bilhah for a wife, and Jacob cohabited with her. Bilhah conceived and bore Jacob a son. And Rachel said, “God has vindicated me; indeed, He has heeded my plea and given me a son.” Therefore she named him Dan.
(maybe what was meant was that his mother was a concubine (he was the first of Yakovs children born not from his first 2 wives))
I've never heard this before, and my explanation isn't terribly convincing even to myself, but here's my attempt for what it's worth.
As hazoriz quotes, Rachel gave Bilhah to Yaakov as his wife. But she didn't have the authority to do that. Only Bilhah herself if she was above 12.5 years old, or her father if she was under 12.5, can accept kiddushin. As Rashi (30:10) says, Zilpah was the youngest of the four wives, but maybe both she and Bilhah were under 12.5 years old, and her father was not able or not willing to marry them to Yaakov. (Especially if their father was Lavan, as per the midrash: he didn't give anything away for free.) Maybe he then changed his mind after his grandson Dan was born, or she turned 12.5 and could marry him herself.
I don't find applications of this kind of halachic reasoning before Matan Torah to be compelling, but this could be what they meant.