1.Capisce persino un po' il dialetto veneto.
2.Respira un po' d'aria fresca.
The answer is simple: the first sentence is uncorrect, although you could find it written in a newspaper or elsewhere. The sentence you wrote could be correct in some dialectical forms, but not in pure italian.
But isn't so simple to explain it to a not-native speaker!
Maybe you don't know that "un po' " is the contracted form of "un poco" (a little, a bit). In a sentence where you use "un po' " referring to an object (so after writing un po' you have to answer to the question "un po' (a bit) of what?) you must start the next preposition with the preposition "di" (or d', if the next word starts with a vowel).
- Vorrei un po' d'aranciata (I'd like some orange juice)
- Giovanni parla un po' di francese (Giovanni speaks a bit of french)
- Ho letto un po' di libri (I have read some books)
But if you use "un po' " and then you put an adjective or an adverb, you don't have to write any preposition.
- Mi sento un po' meglio (I feel a bit better)
- Andrea ha agito un po' precipitosamente (Andrea has acted a bit hastily)
- La tua gonna è un po' corta (your skirt is a bit short)
Therefore, the correct sentence is:
"Capisce persino un po' di dialetto veneto."
In bocca al lupo! :)