Like Return of the Jedi, the title The Phantom Menace is ambigious. There are three characters who could be "the phantom menace": Anakin, who is only a child in this movie but will grow up to become Darth Vader and terrorize the galaxy; Palpatine, who uses his position as a senator to disguise his identity as a Sith Lord; and Darth Maul, who mysteriously appears in order to track down Queen Amidala and harrass her Jedi protectors.
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During their dinner conversation, Padmé tells Anakin, "Our ship was damaged, and we're stranded here until we can repair it," and he replies, "I can help; I can fix anything." His prodigious technical ability seems to be an attribute of his status as the Chosen One. In the same way that he will restore balance to the Force, he can restore balance to mechanical systems and get them to work again.
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While Qui-Gon cleans Anakin's cut, they talk about the stars, and Anakin comments, "I wanna be the first one to see 'em all!" There may be a nascent feeling of conquest in this that's fulfilled later when Anakin becomes Darth Vader and takes over the galaxy with the Empire, but considered together with Anakin's interest in podracing, this also illustrates simply that he has qualities that make him a less than ideal candidate for a Jedi. These are the same qualities that Yoda specifically warns Luke against in The Empire Strikes Back: "Adventure. Heh. Excitement. Heh. A Jedi craves not these things." That Anakin does crave these things may be part of why the Jedi council initially rejects him for training as a Jedi.
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In the movie, the chancellor is referred to only as "Chancellor Valorum," but in the expanded universe, his first name is Finis. Finis valorum is the Latin phrase "the end of values." Finis is a third declension masculine singular noun in the nominative case, and valorum is a third declension masculine plural noun in the genitive case.
Based on the little that's seen of him in The Phantom Menace, it seems that Chancellor Valorum is a chancellor "of values," as his name suggests. (Senator Palpatine tells Queen Amidala that the "accusations of [Valorum's] corruption" are "baseless," but this might just be part of his manipulation.) His name has more significance in light of Palpatine's replacing him as chancellor. Valorum represents "the end of values" because once Palpatine becomes the chancellor, he uses deception to gain power and eventually turns the Republic into the Empire.
Based on the little that's seen of him in The Phantom Menace, it seems that Chancellor Valorum is a chancellor "of values," as his name suggests. (Senator Palpatine tells Queen Amidala that the "accusations of [Valorum's] corruption" are "baseless," but this might just be part of his manipulation.) His name has more significance in light of Palpatine's replacing him as chancellor. Valorum represents "the end of values" because once Palpatine becomes the chancellor, he uses deception to gain power and eventually turns the Republic into the Empire.