>>1
Japanese here.
Stereotypes do exist, but they're not about accents. English intonation and prosody are much more noticeable. Generally speaking, Japanese is "flat" when it comes to intonation, so when Americans speak Japanese as they do English, we think they're placing too much stress on a word. Also, body language looks exaggerated.
Accent wise, the American accents aren't very noticeable to normal Japanese ears. Maybe Americans sound a little more mature than Japanese, but it's not that different.
I think this is because the Japanese language has much fewer phonemes, i.e., Japanese roughly divides the sound spectrum. If you're good at mimicking prosody, it's not that difficult to sound like a native speaker to Japanese monolinguals' ears because your American accent most likely falls within the roughly divided phonemic classes. In fact, your average Japanese can't distinguish the General American from typical British English at all.
Interestingly, my English teacher speaks Japanese pretty well and I thought he had only a slight accent. But as my English improved, gradually my ears became "tuned" and started picking up his accent more. To me, it's like his pronunciation was getting worse each day. Apparently, he was actually getting better because he was living in Japan and talked with us everyday.