Q. I often noticed in others and on myself that as Hallel is recited we may omit or mispronounce some word or letters, especially when one is tired or it is being said too long. Does one comply if he just misses a letter or two?
A. Mishna Berura (488: 2) mentions that if one skipped a pasuk or even one word of Hallel, one has to go back and recite the omission and then repeat the rest in proper order, otherwise one does not comply with the mitzva. Shulchan Aruch Horav (ibid. - 282: 20) mentions that the above applies even if one missed one letter. Shaar Hatzion (488: 2) compares Hallel to the reading of the Megilla, where even one missing letter is essential.
Ishei Yisroel (41: 44), indeed rules that if one became aware of his mistake after finishing the complete Hallel and already recited the last brocho, he has to repeat Hallel again with both corresponding brochos.
However, it seems from Mishna Berura (422: 27) an Biur Halocho (ad loc.) that on Rosh Chodesh, when only the half Hallel is recited, if the above occurred, one should repeat Hallel without a brocho.
Horav Shlomo Miller's Shlit'a opinion is similar.
Rabbi A. Bartfeld as advised by Horav Shlomo Miller Shlit'a