There are a few important oddities occur that when completing the story in an unintended way.
Using Forest Escape to get Zelda's Lullaby before beating the Deku Tree causes some odd side effects. Getting Zelda's Lullaby advances the Kokiri Forest / Sacred Meadow Forest state, which allows you to get Saria's Song. However, because the Forest is still in a pre-Lullaby state, the two states conflict with one another, causing oddities. Saria will still stand in front of your house, but will have the same dialogue as she does in the Sacred Forest Meadow. Mido will no longer block the path to the Deku Tree, allowing you to enter without the Kokiri Sword if you used a Deku Stick to escape the Forest. And probably the most awkward of all, the Kokiri boy that is trying to lift the rock will be making an "odd gesture" towards you...
When you return to the forest after obtaining Zelda's Lullaby, the angle to clip through the Kokiri guard is slightly altered. When you move down-left between the Kokiri guard and the wall before the angle setup, only hold the control stick just past the ESS position so that Link moves very gently into the corner. If you move any faster and get bounced away from the Kokiri guy at all, the escape will absolutely not work consistently.
As for the angle on the wall, it isn't strict at all. Just aim the sword's jewel in the middle of the entire green smudge on the wall, that's it.
The game only checks for the Spirit and Shadow Medallions when determining whether or not to play the cutscene that gives you the Light Arrows. The reason for this seems to be that the developers assumed that the Shadow Temple could not be reached without first obtaining the Forest, Fire and Water Medallions, which triggers the Nocturne of Shadow cutscene. However, it is possible to enter the Shadow Temple without using the song. The Spirit Temple is required because it can be completed at any time, even under normal circumstances.
It is also possible to obtain the Shadow and Spirit Medallions through the use of Reverse Bottle Adventure; have the Broken Goron's Sword on C-right and empty and recatch either Bugs or a Fish on your B Bottle.