Inuyasha

Inuyasha and Kagome share their first full kiss, in this episode.

The Shikon Jewel becomes whole again in this episode.

Sesshomaru gets a new sword in this episode. The sword is Bakusaiga. It can kill thousands of demons with one swing and decompose any organic material which has been cut by the blade. Bakusaiga's ability to decompose organic material is what prevents the regeneration of any demon body part that Sesshomaru cuts off with it.

This episode demonstrates the only time that Kanna has shown disloyalty to Naraku, unlike her other siblings.

Kagome has four arrows in her quiver, and one in her bow. She fires two at the flower prince. Instead of three in her quiver she now has five.

Naraku gains a new power--the ability to create poisonous spiderwebs.

Naraku uses the power that he gained from eating a tree demon, the ability to break barriers akin to the red Tetsusaiga and the Adamant Barrage.

Jaken points out that he's never seen Sesshomaru be kind, which is true on his part, since is usually clobbered in response to accidentally insulting Sesshomaru.

Since the previous season left out the manga plotline where Koga meets the mindless version of Moryomaru, it doesn't make sense as to how Koga knows of him in this series.

It would seem Kagura lives on as her spirit of wind, since her words are heard even after she disintegrates.

Kagura believes she can heal herself in a day from Naraku's miasma, but due to her heart having been returned, she lost the immortality/healing powers she had, previously.

Sesshomaru uses his Azure Dragon Wave technique in this episode (Soryuha in Japanese). The strike appears to be made up of arcs of blue lightning which hit the ground and unleash destruction aimed at the enemy.

This is the first time that Moryomaru uses his attack, Raimeiho.

The first episode has managed to include all of the main characters of the show.

If you pay close attention to the movies they all have a repeated theme: The last bad guy is always killed by a two-weapon combination move, with the Backlash Wave being one of the moves.

The wound that Inuyasha's father received from Ryukotsusei in the episode Father's Old Enemy: Ryukotsusei, allowed his father to be weak enough to be killed in battle with a human during a fire. It is unknown if Inuyasha's father would have survived Ryukotsusei's wound, otherwise.

Since Inuyasha was born the same night his father died, and the spirit in the sheath was only able to keep Sou'unga sealed for 200 years after that (as Myoga stated in the flashback to the conversation about what to do with the three swords following the death of Inuyasha's father), Inuyasha is roughly 200 years old, including the time he spent sealed to the tree by Kikyo's arrow.

Myoga: The Dragon Twister, the attack of a dragon from hell. Its destructive power surpasses that of even the Backlash Wave.

It's odd that Inuyasha's father was unable to fully defeat Ryukotsusei with The Dragon Twister attack when Inuyasha defeated Ryukotsusei with the Backlash Wave, unless you remember that he wouldn't use Sou'unga to kill an enemy, because they then become the walking dead.

Sou'unga was not originally made or forged from one of Inu no Taishou's fangs. He found the sword and kept it, so it wouldn't fall into the wrong hands.

About 25 minutes into the movie, Inuyasha is about to kill a crying child. Miroku takes the prayer beads off of his right arm so that he can stop Inuyasha, if need be. After the camera moves to show Inuyasha's face, then flashes back to the original camera angle, the beads are still in Miroku's left hand.