Yoda teaching the Younglings, and them all helping Obi-Wan, is a purely adorable scene.
Watto seemed genuinely happy to see Anakin again, considering he owned him and Anakin does not return the sentiment.
The Anakin and Padme relationship attracts some bashing, but Padme's Anguished Declaration of Love at the end of the film is actually a bit moving.
And in the picnic scene, Padme asks Anakin if he is going to use his Jedi Mind Trick on her, but he tells her that they only work on the weak minded. While it was clearly meant as love banter, Anakin is communicating that he finds Padme to be a strong-minded person. This might be YMMV, but Anakin is also refusing to use Power Pervision Potential with his Jedi Mind Trick.
Jango Fett may be a ruthless bounty hunter, but you can't deny he's a very doting father to his clone, Boba Fett. Boba clearly adores him in return which makes Jango's death pretty tragic despite him having it coming.
Though this definitely is more of a Tear Jerker than anything else, Shmi Skywalker, after having been tortured by the Tusken Raiders, at the very least, got to see her only son one last time in her final moments.
The secret wedding of Padme and Anakin.
Behind the scenes, Daniel Logan grew up without a father. The first thing Temuera Morrison said to him was that their roles would be easier if they actually referred to each other as "dad" and "son." They've stayed in touch ever since.