Awesome Art: The manga adaptation, which accurately recreates, and even improves some of the frames from the anime.
Jerkass Woobie: Yukiatsu may be an elitist asshole who lives to show Jinta up, but Menma's death left him a whole mess of emotional issues and he does realize how pathetic he is. He does start to get a bit nicer after he is outed as the fake Menma.
Moe: Menma. Also the kids when they were young and Menma's little brother.
Purity Sue: Menma. She has a million good qualities and no real significant flaws. She's selfless, pure, beautiful, innocent, loves everyone unconditionally, and is loved by all in return. Tsuruko and Anaru want to be like her, and Jintan and Yukiatsu are both still deeply in love with her even though she's been dead for years. This can be explained somewhat with her being, well, a pure and rather innocent little kid even by normal standards before her death, and literally not being able to change or mature from there.
She may be a Purity Sue, but she also works as a deconstruction of the trope. Not only was Menma ridiculously pure and innocent (and kinda ditzy) because she died as a child and thus got mentally/emotionally stuck as a little girl forever, but it's made brutally clear how much pressure that kind of character would put on her friends: Tsuruko and Anaru remember Menma fondly but are also jealous and resentful of her because she (unintentionally) left an insanely high standard for them to meet when she kicked it; Jintan and Yukiatsu are very screwed up due to still loving her for a long time after her death, with Jintan unable to function in social situations and Yukiatsu cultivating an unhealthy obsession; and Poppo constantly has to put on a happy face in order to interact with others due to his guilt after not being able to save her life.
Ship Sinking: The end of the series implies Jintan/Anaru and Yukiatsu/Tsuruko, but The Movie outright scuttles the second (Tsuruko confessed to Yukiatsu but in her words "nothing came of it") and fires a supercavitation torpedo at the first, showing that Anaru still has a long way to go before she can confess to Jintan, and Jintan has a long way to go before he can get over his Single-Target Sexuality toward Menma.
Both Jintan and Menma fail to just have Menma prove her own existence to everyone else by simply lifting an object or two in someone's direct line of sight. It's especially noticeable at the end of episode five, when Poppo is intentionally seeking out Menma because he wants to help her grant her wish. Instead of trying to interact, Menma cries over not knowing what she wants to do and instead wishes that she could talk to her friends, leaving Jintan to angrily tell Poppo to stop. It doesn't help that Menma ended up revealing herself in such a way in episode eight.
It's somewhat more understandable when Menma says she has tried to do the same thing in her house, but it doesn't always work. (And it's speculated that this may be because her mothers's grief is too intense to allow Menma to contact her — "Mama gets really sad", remember?). She could have simply assumed it wouldn't work with her friends either, specially considering how much they changed and grew apart after her death, and episode 8's revelation scene came during quite the crisis between the former Peace Busters so she likely used it as a desperate measure.
Jintan has a subconscious desire to keep Menma to herself here amongst the living that he struggles with, and thus monologues that he doesn't really need to think about it; Yukiatsu later discusses this possibility with the rest of the gang after Menma's ghost is proven to be real. Menma simply desires to stay with her friends and also monologues that she doesn't really need to think about it, but she comes to acknowledge that she needs to pass on and fulfill her wish for everyone else to move on. Both were basically Obfuscating Stupidity as to find an excuse not to change the status quo and move on.