The Rambam (Eidut 9:1) lists ten types of people who cannot serve as witnesses: women, slaves, minors, lunatics, deaf-mutes, the blind, wicked people, disgraceful people, relatives, and people with an interest in the case. This time, we will discuss relatives and wicked people.
Who is a relative in these matters? The relationship of brothers is considered a first degree relationship (rishon b’rishon). The son of one of the brothers with his uncle is called a first with a second (rishon b’sheni). First cousins are second with second (sheni b’sheni). These relationships all disqualify one to testify. The next level of relationship, namely the grandsons of brothers (second cousins) or third with third (shlishi b’shlishi), does not disqualify. Even the grandson of one brother with the son of another (sheni b’shlishi) does not disqualify. These rules are even for a "half" relationship, based on brotherhood through a father or a mother alone. Also, "a husband is like his wife." This means that when two people are close enough, the disqualification applies to their spouses as well. However, the relatives of the spouses are fit to testify for or against their in-law’s relatives.
In addition to not testifying about a relative, two relatives may also not testify together about any issue. Furthermore, witnesses may not be relatives of the judges (who also may not be each other’s relatives).
The Torah says: "Do not place your hand with a rasha (wicked person) to be a corrupt witness." Chazal learn from this that a rasha is disqualified to serve as a witness. In this regard, one who violates a negative commandment that carries the punishment of flogging is a rasha. If one violates rabbinic prohibitions, he is unfit on a rabbinic level. The Amoraim dispute whether the "wickedness of corruption" refers only to one who sins for monetary gain or whether anyone who willfully violates a Torah law is disqualified (we accept the latter view). Some Rishonim say that a rabbinic violation and disqualification applies only if he violated it for a specific gain. Thus, for example, one who signed as a witness on a loan contract that includes usury (which is rabbinically prohibited) is not disqualified (Rama, Choshen Mishpat 34:3). Another difference between one who violates a rabbinic prohibition as opposed to a Torah-level one is that he is disqualified only if beit din formally pronounces him to be unfit, which rarely transpires in our times.
Finally, in order for one to be disqualified as a rasha, he must be fully aware that the action he performed is a sin. The logic of the disqualification is that someone who does not care about his moral obligations may not care about the need to testify truthfully. This contradicts the absolute credibility the Torah awards fit witnesses. There is no reason to suspect though that one who violates a prohibition he was not fully aware of will violate the prohibition of testifying falsely given that the latter is something that all understand.