The second sequence shows Homura fighting off against a powerful floating...thing. Homura in later Episodes tells Madoka that a something powerful is coming soon. Episode 10 reveals that the Witch from Episode 1 was actually Timeline 4 Walpurgisnacht.
Madoka asks her mom about her ribbons. She wonders if her ribbons will make her look cool and stand out above the crowd at school. The final episode has Madoka giving Homura her ribbons. Then, Homura meets Madoka's mother (or at least, the woman who was Madoka's mother when Madoka still existed as a person), who remarks that the ribbons look uncannily like something she would make her daughter wear, if she had one.
The entire introduction sequence for Homura at school has her doing incredible stunts and then proceeding along a walkway to the nurse's office with Madoka, the designated class nurse. Strangely, Homura is breaking down along the way while Madoka gives heartfelt encouragement. The first few minutes of Episode 10 has this whole sequence replicated but with reversed positions and Homura being the exact inverse she was in the current timeline. In particular, the dramatic shot of Homura turning on her heel (literally) to face Madoka appears again in episode 10, with their roles reversed.
Kyubey is running from Homura in the air shaft in the mall, with the intent to kill him. Kyubey, at this point in time, looks extremely hurt and defenseless, while Homura already looks like an Anti-Hero. She was doing it to try to prevent Kyubey from making a contract with Madoka, knowing what would happen if she didn't. In the Drama CD, Madoka used her wish to save a cat from death, with Homura appalled for such an innocent wish. In Episode 10, Madoka is shown to be an very kind and caring person.
Episode 1's Witch has copious amounts of flowers and scissors stylized like a "secret garden" Eldritch Location, but Mami defeats this Witch. Episode 3 has Level Ate, complete with knives and cakes. Episode 3 was also the episode that had the Off with Her Head! with Mami. There's also a taboo about cutting off the heads of flowers.
Mami Tomoe's name is stylized in a strange way on the plaque at the apartment she lives in. Her name is written like "巴マミ", and "Tomoe" is also the same name of a famous female samurai named Tomoe Gozen. Her name turns into a Visual Pun when her head gets chomped off. This is also a reference to Tomoe Gozen, who was a One Woman Army who defeated thousands of enemies and returned with the head of one of the enemies.
Mami also explains that the Soul Gem is formed as proof of a contract with Kyubey. Eventually we learn that it's Exactly What It Says on the Tin. The Soul Gem literally contains the magical girl's soul, to help them with pain tolerance, as Kyubey demonstrates with Sayaka Miki.
In one part Sayaka asks something along the lines of "How are witches different from magical girls?", apparently not by much.
Remember the teacup Mami summoned after defeating Gertrud in Episode 2? It reappears in Episode 3 after Homura blows up Charlotte, the witch that ate Mami. It's broken. Also, Homura said that "this is the fate of a magical girl", while it shows what's left of Mami (blood and a broken teacup) and a Grief Seed.
Before Mami arrives at the room that has Charlotte, she says that to celebrate Madoka becoming a magical girl, they should eat cake. In Episode 12, when Madoka is in the meta-world talking with Mami and Kyoko, Mami is serving her cake - right before she becomes a magical girl.)
Madoka asks how to deal with Sayaka, who keeps fighting for what she thinks is right, but the more effort she puts into it, the worse things turn out for her. Madoka's mother suggests to do the wrong thing to snap her out of it. During Episode 8, Homura threatens to kill Sayaka Miki if she keeps troubling Madoka with her self-destructive behavior. The look on Sayaka's face shows that doing that actually got her attention. If saving Sayaka was Homura's true intentions, then it might have actually worked if Kyouko didn't pull a Big Damn Heroes moment by restraining Homura.
The OP itself turns out to be a Brick Joke when it's shown at the end of the episode instead of the beginning, to reveal that the entire song had always been from Homura's point of view, not Madoka's. This wasn't exactly obvious before, since shots of Madoka take up about 99% of the OP; but the 10th episode is all about Homura, and the OP's lyrics are practically a plot summary. Like This