Beitzah, Chapter 1, Mishnah 5. This mishnah lists several disputes between Beis Shammai and Beis Hillel regarding the laws of Yom Tov.
Removing shutters on Yom Tov:
"Beis Shammai omrim: ein mesalkin es hatereisin b'Yom Tov" - the tereisin are the doors that closed a cabinet or chest used by merchants to store their merchandise. According to Beis Shammai, these doors may not be removed on Yom Tov.
"U'Beis Hillel matirin af l'hachazir" - according to Beis Hillel it is permitted to remove them, and even to put them back in place on Yom Tov.
The reason for the leniency: since opening the chest is needed in order to obtain food, if putting the doors back were not permitted, there would be a concern that a person would refrain from removing them in the first place, and the joy of Yom Tov and the pleasure taken in it would be diminished. For this reason it was permitted.
The Gemara explains that the dispute applies only in one particular case, and everything depends on the type of hinge in the shutter:
No hinge at all: even Beis Shammai agree that the shutters may be removed and put back, and there is no concern.
A hinge at the corner on the side: a more substantial and permanent hinge. Here even Beis Hillel agree that they may not be put back, because it looks like building. Some explain that the reason is the concern that this will lead a person to make an actual permanent repair - to take a nail and hammer it in.
A middle hinge: a hinge that is not entirely permanent, but which carries a certain concern of appearing like building. This is the subject of the dispute: Beis Shammai did not permit it, and Beis Hillel permitted it.
Moving the pestle on Yom Tov:
The next dispute deals with the question of whether one may move a large crushing implement, the pestle, on Yom Tov. "Ein nosnin es ha'eli" - according to Beis Shammai one may not move the large wooden pestle, which is normally used for crushing, even when his intention is "lekatzev alav basar" - to cut meat on it, which is a permitted activity, whereas crushing may not be permitted on Yom Tov, depending on what is being crushed.
"U'Beis Hillel matirin" - it is permitted, since this is needed for the joy of Yom Tov and the pleasure taken in it, in order to prepare the meat. And even though this is a utensil whose primary use is for a forbidden activity, a utensil designated for crushing that is not permitted, it may be moved for its own use, in order to employ it for a permitted activity - and this is one of the criteria that apply on Shabbos as well.
Placing the hide before those who tread on it:
"Beis Shammai omrim: ein nosnin es ha'or lifnei hadarsan" - one may not place the hide of an animal slaughtered on Yom Tov in a place where people tread on it. "V'lo yagbihenu" - and one may not even lift it, since it is muktzeh. "Ela im kein yeish imo kezayis basar" - unless there is a kezayis of meat attached to it, which makes it subordinate to the meat and thereby permits moving it.
"U'Beis Hillel matirin" - it is permitted to move the hide itself, even without meat attached to it.
The purpose of placing it in a spot where it would be trodden upon was part of the process of preserving the hide, which would otherwise be liable to spoil. Beis Hillel were concerned that if they did not permit this, people would refrain from slaughtering animals on Yom Tov out of fear that the hide would be ruined, and they would thereby be deprived of the joy of Yom Tov and of the slaughtering of the meat they need. They therefore permitted even placing it before those who tread on it on Yom Tov, even though this is a form of preparing the hide for tanning.
Carrying out into a public domain on Yom Tov:
"Beis Shammai omrim: ein motzi'in lo es hakatan, v'lo es halulav, v'lo es sefer haTorah lireshus harabim" - according to Beis Shammai, one may not carry anything out into a public domain on Yom Tov except for the sake of food preparation alone, that is, for the sake of actual eating.
"U'Beis Hillel matirin" - for in their view, "mitoch shehutrah hotza'ah l'tzorech, hutrah shelo l'tzorech": since carrying out was permitted for the sake of food, it was permitted even not for the sake of food - provided that there is some positive need involved, such as the need of a mitzvah (a lulav or a sefer Torah) or something that provides pleasure (taking a child out for a walk). But something for which there is no need at all may not be carried out.
In summary: this mishnah lists four disputes between Beis Shammai and Beis Hillel in the laws of Yom Tov: removing the shutters and putting them back, which depends on the type of hinge; moving the pestle in order to cut meat, which was permitted under the rule of moving a utensil whose primary use is forbidden for its own use; placing the hide before those who tread on it; and carrying out into a public domain, which was permitted under the rule of "since carrying out was permitted for the sake of food, it was permitted even not for the sake of food." The common thread running through the leniencies of Beis Hillel is the concern that withholding the leniency would detract from the joy of Yom Tov and from the pleasure taken in it.