One of Mandarin's biggest characteristics is its tones. Other Sinitic dialects/topolects aren't any different: Cantonese, Hakka, etc.
Are there any toneless Sinitic dialects/topolects? (Japanese?)
In modern Shanghainese and some other of Wu dialects, the adherence to the five tones has basically diminished in speech (still exists when referring to single characters), and converted into three pitches(low, mid, high).
Pitches for the same character, however, do vary through speech. For example, notice how the pitch for character 大's one pronunciation "da" differ from word to word: first the characters, then Shanghainese and corresponding pitch, then meaning, and finally the character's Mandarin Pinyin.
(I'm not using any established romanization system for Shanghainese, instead I just used my own way for this ad hoc purpose.)
I couldn't find the definition to "pitch accent language," so I can't answer you whether Shanghainese has become one.