Gemara

102b (Mishnah): One is liable for Makeh b'Patish (making a final blow with a hammer);

R. Shimon ben Gamliel says, even one who bangs a hammer on an anvil [and not on the Kli being made] while making the Kli is liable, for this improves the final product.

(Rav): If one drives a peg into the handle of a hoe [so the blade will not fall off], he is liable for building;

(Shmuel): He is liable for Makeh b'Patish.

103b (Beraisa): One is liable for any amount of drilling, scraping, tanning, or making any design on a Kli;

R. Shimon says, he is not liable unless he drills, scrapes, tans, or draws as much as he intended.

75b (Rav Yehudah): If one cuts off Akufi (strands that hang from a curtain; alternatively, protrusions from a garment), he is liable for Makeh b'Patish;

This is only if he is insistent to remove them.

147a (Rav Huna): If one shook out his Talis on Shabbos, he is Chayav Chatas.

This is only if it is new, black, and he is particular. If it is old, white or red, or he is not insistent, it is permitted.

Ula came to Pumbadisa and saw Rabanan shaking out their garments. He said 'they are Mechalel Shabbos!'

Rav Yehudah: You may shake out right in front of him. We are not insistent.

Rav Yosef asked Abaye to bring his hat; Abaye saw dew on it, and was hesitant.

Rav Yosef: Shake it out. We are not insistent!

Rishonim

Rambam (Hilchos Shabbos 10:16): One who bangs once with a hammer is liable. And anyone who does something that is final Melachah is liable for a Toldah of Makeh b'Patish. E.g. one who makes a design on a Kli, even part of a design, is liable.

Rambam (18): If one cuts off Yevolos (protrusions) from a garment, e.g. what is common on wool garments, he is liable for Makeh b'Patish. This is only if he is insistent to remove them. If he removed them while involved with something else [unaware that he is removing them], he is exempt. If one shook out a new black Talis on Shabbos to beautify it and remove the Tzihuv Lavan hanging from it, like the craftsmen do, he is Chayav Chatas. If he is not insistent, it is permitted.

Me'iri (75b DH ha'Tzar): The Kli was complete, and the design beautifies it. Since the Kli does not need it at all, this is Makeh b'Patish. This is not only for finishing the design, rather, even for beginning it. Below (103b) we obligate for any amount of a design. Every final Melachah is not finished at once. Even banging a hammer is done more than once. The Ra'avad says so.

Shiltei ha'Giborim (42b:4, cited in Magen Avraham OC 302:5): If one removes a tailor's Shalal (coarse stitches used to attach pieces that must be sewn together, until the tailor will sew them nicely with fine stitches - Machatzis ha'Shekel), also this is final Melachah. I am unsure whether he is liable. I lean to be stringent [but surely he is not liable - the Magen Avraham omitted these words] if he is not particular about it.

Poskim

Shulchan Aruch (OC 302:1): One who shakes out a new black Talis from the dew on it is liable, for shaking is good for it like laundering. This is if he is particular not to wear it without shaking it out.

Rema: One may remove feathers from a garment on Shabbos.

Kaf ha'Chayim (10): This refers to feathers from pillows and blankets, which are not Muktzeh.

Kaf ha'Chayim (11): One should not remove anything hanging on a black garment.

Shulchan Aruch (2): If one removes Yevolos from a garment, e.g. those on wool garments that remain after weaving, he is liable for Makeh b'Patish.

Beis Yosef (DH ha'Notel): Rashi explains that Rav Yehudah discusses cutting off strands that hang from a curtain. They are in the place of the knots, where a thread snapped and was tied. Similarly, after it is woven we remove straw and chips that were unintentionally woven in. This is the final Melachah. He is liable for Makeh b'Patish.

Gra (DH Yevoles): The Shulchan Aruch explains 'Akufi' like the Rambam.

Kaf ha'Chayim (14): One should be stringent for both Perushim. However, if a chip became inserted in a garment after it was finished, Makeh b'Patish does not apply to removing it.

Mishnah Berurah (8): Yevolos are like Yaveles, i.e. protrusions. Perhaps one is liable for removing Shalal, for the craftsman removes it when the finishes the work.

Shulchan Aruch (ibid.): This is only if he is insistent to remove them. If he removed them Derech Esek (while involved with something else), he is exempt.

Beis Yosef (DH ha'Notel): It seems that the Rambam explains 'he is particular about them' excludes one who removed them without intent to beautify the garment, rather, like Misasek. However, if he intentionally removed them, even if he would not have refrained from wearing the garment without this, he is liable.

Kaf ha'Chayim (16): The Beis Yosef rules like the Rambam, and exempts only if he was Misasek, and he would not have worn the garment even without this.

Note: I do not understand this. It seems that the Beis Yosef exempts Misasek, whether or not he would have worn the garment without this!

Beis Yosef (DH v'Chasav): After this, the Rambam wrote that if one shook out a new black Talis... to remove the Tzihuv Lavan, he is Chayav Chatas. If he is not insistent, it is permitted. It seems that this is due to Makeh b'Patish, just like removing Yevolos. However, I am unsure whether he explains 'particular' to mean anything other than Misasek, like removing Yevolos from garments.

Taz (2): 'He is particular' means that he would not wear the garment without this, therefore he intentionally removed them. 'Derech Esek' means that would wear the garment without this. He does not remove them with intent to fix the garment, rather, like mere Misasek, so he is exempt. If so, 'he is not particular', which is from the Rambam, is just like 'he is particular' in Sa'if 1. There was no need for the Beis Yosef to distinguish them.

Gra (DH Yevoles): The Rambam connotes that also in Sa'if 1, 'particular' is anything but Misasek. The Beis Yosef was unsure. This is only based on his opinion that he rids it of the Tzihov Lavan, like craftsmen, and he is liable for Makeh b'Patish. Rashi and Tosfos explain that Sa'if 1 is due to laundering. It has no connection to this Sa'if.

Mishnah Berurah (10): This is final Melachah more than Sa'if 1, therefore he is liable even if he would wear it without removing them. Only Misasek is exempt.

Bi'ur Halachah (DH ha'Loket): The Mishbetzos Zahav (2) was unsure if one is liable only for removing all the Yevolos that there are, or even for removing one, even if many remain. I bring a proof from one who makes a picture on a Kli. He is liable for any amount, due to Makeh b'Patish (75b, Rambam 10:16). The Chiyuv for Makeh b'Patish is even for part of the final Melachah, since it is one of the actions done when the Kli is finished. Do not explain that it refers to the last part of the design, for R. Shimon argues, and exempts until he draws all of it. This shows that the first Tana obligates even for the first part. I later found that the Me'iri says so.

Magen Avraham (5): Stains that remain from our weaving have the same law as Yaveles. Sefer ha'Zichronos forbids even if he is not particular.

Kaf ha'Chayim (20): It is forbidden to remove them in the way of Misasek.

Magen Avraham (5): If flax seed or a cooked food came on one's garment, one may peel it off.

Mishnah Berurah (11): If the garment is new and new, one may peel it off only if he is not particular. If it is moist, one cleans it with a rag.

Bi'ur Halachah (Sa'if 1, DH Aleha): Bahag says 'one may shake out a Talis like Rav Yehudah. If flax seed or a cooked food came on his garment, he may peel it off.' What is his source regarding flax, and why did he teach it with shaking out? I say that he learned like R. Chananel. He says that Abaye saw filth on Rav Yosef's hat. (Also the Me'iri and Chidushei ha'Ran explain like this.) Bahag permits shaking out, for we are not particular, like Rav Yehudah. After this, he alludes to the episode with Rav Yosef. Also there, it is permitted because we are not particular. Therefore, if one is particular not to wear the garment without peeling it off, it is forbidden, just like shaking, for the Gemara put these together. The Acharonim did not explain Bahag well enough. According to Bahag, why do we permit scraping mud on a garment with one's fingernail? Why is this better than flax seed or a cooked food on his garment? Indeed, I say that also regarding mud Bahag permits only an old garment, or if he is not particular. A better answer is that scraping off mud does not totally remove the stain; we discuss wet mud. Therefore, this is not laundering. Peeling off the flax seed or cooked food totally removes the stain, therefore we permit only the way we permit shaking out a Talis, i.e. it is old or he is not particular.