Mishnah 6 in the first chapter of Maseches Terumos lists five categories of people who may not separate Terumah at the outset, yet if they did separate it after the fact, their Terumah is valid. The words of the Mishnah: "Chamishah lo yitromu, ve'im tarmu - terumatan terumah" - five may not separate Terumah, and if they separated, their Terumah is Terumah.
Two reasons underlie this list:
The obligation to recite a berachah: Like many mitzvos, separating Terumah requires a berachah beforehand, as was explained earlier in the maseches. Someone who is unable to recite the berachah does not separate Terumah at the outset, since he will not be able to make the berachah. But since the obligation of the berachah is only rabbinic and does not affect the fulfillment of the mitzvah itself, one who did not recite it has fully performed the mitzvah of the Torah. Three of the five are listed for this reason.
Choosing the finest portion: One is obligated to select the choicest of the produce and separate that as Terumah, as it says: "All the Terumah of Hashem, from the best of it" - from the "cheilev," the best and finest part. Someone who is unable to determine which part is the finest should not separate at the outset, since he will inevitably fail to choose the choicest. Nevertheless, after the fact, whatever portion he selected becomes Terumah according to halachah.
The five categories:
"Ha'ilem" - the mute person, one who cannot speak. He hears perfectly well, but he is unable to produce speech, and therefore he cannot recite a berachah - and so at the outset he should not separate Terumah.
"Vehashikor" - the drunk person. In defining a person's drunkenness, Chazal established two levels:
"One who cannot speak before a king because of his drunkenness": a person who is unable to conceal his drunkenness while standing before a king. It is not respectful to appear before a king in a drunken state, and were the king to detect his drunkenness, he would be in danger of the king declaring, "Cut off his head." At this level a person is still entirely responsible for his actions, is obligated in all the mitzvos, and his mitzvos count, with a few exceptions: the most prominent being that he no longer davens Shemoneh Esrei, since it is not fitting to stand before the King of kings while drunk, all the more so when he cannot even stand before a king of flesh and blood. Regarding Terumah, the ability to discern the choicest portion is required, and the drunk person is impaired in this - therefore he should not separate at the outset, but after the fact his Terumah is Terumah.
"The drunkenness of Lot": based on the account in Bereishis concerning Lot, whose daughters gave him wine to drink and in his drunkenness he lay with them. At this level a person has no idea at all what he is doing, and his status is that of a shoteh: exempt from all the mitzvos, and his actions carry no weight at all, since he is not of sound mind. Our Mishnah, then, is dealing with the first level - where, even though the person is obligated in mitzvos, his discernment is impaired and he does not separate Terumah at the outset, while after the fact his Terumah is Terumah.
"Veha'arom" - one who is unclothed. One may not recite a berachah while naked, and the source is the pasuk: "For Hashem your God walks in the midst of your camp to save you and to deliver your enemies before you... and no ervah (nakedness) of any matter shall be seen among you" - the camp must be holy. "Ervah" means something unfitting, and also something indecent, and the word carries a connotation of sexuality. From here Chazal derived that the sexual organs are called ervah, and they expounded "davar" (matter) also in the sense of dibbur, speech - that one may not say words of holiness in the presence of ervah.
The measure in this matter: even a person's own ervah presents a problem. He must cover the ervah, and there must also be a separation in the line of sight between his heart and chest and the ervah. Wearing undergarments alone is sufficient, and he is then no longer considered naked and may recite a berachah; likewise, if he is wearing something long, he is covered even though he has no shirt on. But if he is not covered at all and his ervah is exposed, he may not recite a berachah - and all the more so he should not separate Terumah and forgo saying the berachah.
"Vehasuma" - a blind person. He too cannot determine what is "chelbo," the best part of the produce, and therefore he should not separate Terumah at the outset.
"Uva'al keri" - one who has had a seminal emission, for whatever reason. The point here is not his tumah, which is not relevant to our subject, but rather the enactment from the days of Ezra, that a ba'al keri first immerses in a mikvah before saying anything holy - berachos, tefillah and the like. Since he cannot yet recite a berachah, he should not separate Terumah.
According to the Mishnah's assumption, a ba'al keri contemplates the words in his heart only: he thinks the words in his mind, and does not pronounce them with his mouth.
In summary: the five people listed in the Mishnah are listed on the strength of two reasons alone - three who cannot recite a berachah (the mute, the naked person and the ba'al keri), and two who cannot determine which is the finest portion (the drunk person and the blind person). Since neither of these impediments prevents the actual fulfillment of the mitzvah, the result is that at the outset they should not separate Terumah - but if they did separate, their Terumah is Terumah.