Gemara

(A reciter of Beraisos): If one erred (while saying Shema) and does not know exactly where:

If he was in the middle of a Perek, he should return to the beginning of that Perek;

If he was between Perakim, he should begin with the second Perek.

Rishonim

Rambam (Hilchos Keri'as Shema 2:11): If one read a Parshah (that should be read later) before another, even though he may not do so, I say that he was Yotzei, for they are not adjacent in the Torah.

Rambam (13): If one read Shema but erred, he returns to where he erred. If he is unsure which Parshah he finished, he returns to the first Parshah, i.e. v'Ahavta.

Kesef Mishneh: R. Mano'ach says that if one erred about the words or letters, i.e. he skipped one or two, and all the more so if he skipped a verse, he returns to where he erred and reads from there.

Rosh (2:12): We say that one who erred in the middle of a Perek returns to the beginning of that Perek. This is when he does not know where he erred. If he knows that he said this Perek and remembers that he skipped a verse or a word, he repeats from that verse and onwards. A Tosefta says so. The same applies to Hallel, Megilah and Tefilah.

Poskim

Shulchan Aruch (OC 63:4): If one read the first verse without Kavanah, he was not Yotzei. He returns and reads it again.

Magen Avraham (6): If after finishing he remembered that he read the first verse without Kavanah, it is as if he did not read it, therefore he returns to the beginning.

Eshel Avraham: He must repeat the entire Parshah, for if not, he read it out of order. I am unsure if it is mid'Oraisa or mid'Rabanan that he was not Yotzei.

Shulchan Aruch (64:2): If one read a Parshah and erred and knows where, e.g. he read the entire Perek but skipped a verse in the middle, he returns to the beginning of that verse and finishes the Parshah.

Levush (2): If he skipped one verse or word, he returns to the beginning of that verse or word and finishes the Parshah.

Mishnah Berurah (5): If one omitted one word, some say that it suffices to return to that word and finish from there, if it begins an independent matter, e.g. in the verse "V'Shinantam" he omitted "v'Dibarta". However, Eliyahu Rabah brought from several Rishonim that he always returns to the beginning of the verse.

Mishnah Berurah (6): It is not enough to say just the verse he omitted, for then he did not read in order. However, if he remembered that he skipped a verse in the first Parshah after he said the next Parshah, it suffices to say from the omission until the end of the Parshah, for he need not say the Parshiyos in order.

Gra: A Tosefta (2:4) says that if one read out of order, he was not Yotzei. The same applies to Hallel, Tefilah and Megilah. If one read Shema, erred and omitted a verse, he begins from that verse and finishes until the end. If one entered a Beis ha'Keneses and they already read half, and he finished with them, he goes back to the beginning and finishes until the end. The same applies to Hallel, Tefilah and Megilah. It seems that this is unlike the Rambam (and Shulchan Aruch in Sa'if 1, who explicitly say that the order of the Parshiyos is not Me'akev). The Tosefta discusses omitting a verse, or entering in the middle..., i.e. even in the first Parshah. Even so, he must finish until the end.

Bi'ur Halachah (DH Af): If one read only the first Parshah, in any case he has the Mitzvah of Kabalas Ol Malchus Shamayim, even if he did not read the second Parshah of Kabalas Ol Mitzvos. Even if we will say that both are mid'Oraisa, they are not Me'akev each other. Distinct verses command saying the first Parshah ("v'Hayu ha'Devarim ha'Eleh... Al Levavecha") and the second Parshah ("v'Samtem Es Devarai Eleh Al Levavechem"). Each Parshah has its own theme. Therefore, v'Hayu obligates (saying in order) only the verses in each Parshah, but not to say the Parshiyos in order, and all the more so if only the first Parshah is mid'Oraisa.

Mishnah Berurah (4): The Pri Chodosh says that this is only if he erred. If he was Mezid, he returns to the beginning, like we say about Tefilah (104:7). The Magen Avraham there was unsure about this.

Shulchan Aruch (ibid.): If he does not know where he erred, he returns to the beginning of that Perek.

Levush (2): If one erred in the middle of the first Parshah, but does not know where, he returns to v'Ahavta. We apply Chazakah to say that he read the first verse according to Halachah, i.e. with intent.

Bach (3): It seems that the Tur means that if one is in the first Parshah and knows that he skipped a word or verse, but does not know which, he returns to the beginning of Keri'as Shema. This is like our texts of the Gemara, which say 'he returns to the beginning.' This connotes to the beginning of Keri'as Shema. This is astounding. If he is unsure whether he read the first verse, even if he read it, surely he did not have Kavanah in it, so he must return to the first verse and say everything. If not, he reads out of order! Why does the Gemara say that he is unsure where he erred? Even if he knows where he erred, since he read the first verse without intent, he must return to the first verse! Rather, we must say that he read the first verse with intent, and read afterwards without intent. The Tur means that he returns to the beginning, i.e. to v'Ahavta. We must say the same in the Gemara, that he knows that he read the first verse with intent.

Taz (1): Surely, if this occurred in the first Parshah, he does not return to Shema Yisrael, for one opinion forbids repeating the first Parshah! Rather, he begins from v'Ahavta.

Be'er Heitev (3): The Taz holds like the Bach. He discusses one who knows that he said the first verse.

Kaf ha'Chayim (8): The other Meforshim say that the Taz holds like the Levush, that we assume that he said the first verse properly. Many hold like the Bach.

Mishbetzos Zahav (91:1): The Bach and others say that if one has a Safek whether or not he read the first verse, he must read again, for surely he did not have Kavanah. Alternatively, we leave him on his Chazakah. How can they explain "one who is unsure whether or not he prayed does not pray again"? The Gemara holds that one must have intent in the entire Tefilah. If he did not, he prays again (because he did not have intent in Avos)!

Note: R. Akiva Eiger (here) cited this without comment. We hold (107:1) that who is unsure whether or not he prayed does pray again! Amora'im argue about this (Berachos 21a), but all agree that one who is unsure whether or not he read Shema reads again. Perhaps one opinion is lenient about Tefilah because it is only mid'Rabanan, and there is concern for Berachos l'Vatalah. We rule that one repeats both, for surely he did not have Kavanah! Perhaps Mishbetzos Zahav asks as follows. 1) It is difficult to say that the Amora'im agree about Keri'as Shema for different reasons. 2) If the Bach's reason were true, all should agree to it. 3) The Gemara said that R. Yochanan holds that one repeats also Tefilah, for 'if only one would pray the entire day!' It connotes that he disagrees only for this reason. I answer that the Bach discusses one who is amidst Keri'as Shema. One who had proper Kavanah in the first verse could not forget this so soon. The Amora'im discuss one who is unsure whether he said Shema at all. This can be hours later, e.g. one wakes up in the middle of the night, and is unsure whether or not he said Shema before he went to sleep. One could forget in such a case! One could explain that the Amora'im argue about one who has a Safek whether he was Yotzei Shema, e.g. perhaps he read before the time for Keri'as Shema, or perhaps there was excrement nearby... The Gemara connotes slightly unlike this.

Mishnah Berurah (7): He must return to the beginning of the Parshah due to Safek. Even according to the opinion that the second Parshah is mid'Rabanan, since he is engaged in Keri'as Shema, he must fix everything. In the first Parshah, if he remembers that he said the first verse and Baruch Shem... with intent, he returns to v'Ahavta. If he does not remember that he said the first verse with intent, in any case he returns to the beginning. Reading it without intent is like not reading it at all. He must read the entire Parshah, so it will be in order. He reads the first verse quietly, or waits a little, lest it seem that he says Shema Shema.

Shulchan Aruch (3): If one erred between Parshiyos, i.e. he knows that he finished a Parshah, but does not know if it was the first or second, he returns to the first and says v'Hayah Im Shamo'a.

Beis Yosef (DH Ta'ah): Rashi explains that he returns to the first Hefsek between Parshiyos, i.e. v'Hayah Im Shamo'a. The Rambam holds that he returns to v'Ahavta. Since one must pause between l'Olam va'Ed and v'Ahavta, this is the first Hefsek. Since he knows that he read at least one Parshah, he need not return to Shema. It suffices to return to v'Ahavta.

Mishnah Berurah (8): This is when he does not remember saying even one word from the second Parshah, and he did not say the word va'Yomer. If after he said this a doubt arose, we assume that he said the second Parshah, like normal (before saying va'Yomer).

Kaf ha'Chayim (10): The Bach, Eshel Avraham and Kisei Eliyahu rule like the Shulchan Aruch. Olas Tamid, Orchos Chayim and Kolbo are stringent, like the Rambam. The Rambam agrees that if he knows that he finished the first Parshah, he goes back to v'Hayah Im Shamo'a.