I found pinyin indispensable for learning Mandarin. I agree with Mize that learning Hanzi was invaluable, and that's why I took courses that actually taught reading/writing Chinese characters. Many Mandarin classes teach what I'd call "tourist Chinese", you know, enough phrases to get you through a 2 week vacation.
But for me, language is holistic, and you need to read, write, listen, and speak.
However, written chinese being a "silent" language, there's no way in the world I could learn new Chinese words without Pinyin. Now when I encounter a new character I don't know, I just look up the pinyin for it, and I can pronounce it. (I noticed many Mandarin schools around here start with the bopomofo character system, so as to not confuse kids learning English alphabet with two differing sets of sounds)
One of the difficulties I have with listening to Mandarin speakers is the huge range of diversity in accents they have. I learned Mandarin from a Beijing speaker. Now, when I hear speakers from Sichuan, Hunan, and Shanghai, I find it difficult sometimes to adjust, I guess it's like trying to understand English spoken by someone with a Cockney accent.
A typical example is that Beijingese speakers have these "R" sounds, like
是 (shi) sounds like "Sher" or the "Shir" sound in "Shirt", but my wife, who is Shanghainese pronounces it more like "She", and so does my 2 year old son,
yet I still find myself saying to him “是不是爸爸的车车?" that comes out like "ShiR bu ShiR baba de che che" Can't shake that damn beijingnese R now. Same problem with Nar, Dianr, Liaotianr, Wanr, etc.