Normally, when in the 1st cycle of Clock Town as Deku, one must acquire the Bomber's code, Moon's Tear and Town Title Deed to get up to the top of the Clock Tower.
However, this can all be skipped by performing a Gainer right under the platform to grab the ledge. This saves a significant amount of time because the first two and half days can be skipped right away by listening to Anju's Grandmother's stories then dancing with the Scarecrow until the night of the last day.
Below is a video showing the trick and how to perform a Gainer:
Normally, the entrances to Clock Town are raised up onto small platforms, but it is still possible to get inside from the West Clock Town entrance with a day transition quirk.
Position Epona close to the entrance of West Clock Town and dismount her. Go right next to the loading zone and climb onto her when the clock hits between 5:58 to 5:59 PM. If she happens to neigh during 5:58 PM, you cannot climb onto her which makes it possible to miss the trick.
If done correctly you should get the day transition during the climbing animation. This causes Link's position to be reset back to where he climbed from, but while still on Epona. From there, you can just ride into the loading zone if you climbed from far enough back.
Normally during the first cycle there's no way to exit Clock Town as Deku until Cycle 2, but with a game exploit, you can escape Clock Town as Deku in the 3rd day of Cycle 1 at midnight.
This happens only in the Bombers' Hideout because when the cutscene starts the game has to place you somewhere in the map where the cutscene is currently playing at (which in this case is the Termina Field map). Then after the cutscene is over your last entrance does not change, so dying (or voiding out) will put you in the last entrance.
Another way to escape is, backwalking into the guard when daytime hits. Because of Deku having bad acceleration in MM3D you need to do a sidehop to make it past the guard in time. Home Buffering is recommend because you need to be fast to get past the guard.
Using Flower Sliding, you can clip through the guard in North Clock Town.
Normally, when performing the Moon's Tear Skip, playing hide-and-seek with the Bomber's is skipped meaning entering the Bomber's Hideout would be impossible without going into Termina Field.
But by performing Down A in East Clock Town, it is possible to walk through the Bomber blocking the entrance to their hideout.
It is possible to enter Kafei's room early anytime without having to deliver the letter to Kafei with either of the two methods.
When you turn into Zora and make a sidehop next to the wall in the entrance of the Laundry Pool, you will grab the ledge of the wall and can climb up. From there, walk/run next to the edge until you reach the other side of the map, then either turn into Deku to hop on the water and enter the loading zone or make a sidehop and a Jump Attack to hit the loading zone.
By doing a Goron Pound into the tree in the Laundry Pool, you can get on top of one of the branch. After that, turn into Link and do a Long Jump at the end of the branch to cross the gap and grab the ledge.
Then just normally walk around to the other side of the map to go into the loading zone.
Milk bar clip is a trick that used to be done in the Any% route of the game, because from here we can wrong warp to Stone Tower Temple.
When you load a new area while riding epona, Link will always unmount Epona from the right side. Also, if you L target while on Epona the direction in which you first target will get stored, so when you unmount Epona Link will rotate to that specific direction. Using this, we can clip into the wall next to the door and with a jump slash, hit the loading zone.
By doing a set of Mask Jumps, you can clip into Milk Bar. Note: To do consecutive mask jumps, you either need a New Nintendo 3DS or a Circle Pad Pro attached to your 3DS.