regarding that, I used to have a quite heavy american accent, partially because my mom is american and I grew up listening to country music when I was a little kid (don't judge me
), and I remember it being ostracized by many of my teacher and professors. Especially at highschool and university, though they couldn't actually penalize me for it because I did speak very fluently, a lot of professors sneered at my american accent... not for that particular reason, I think my accent has changed quite a bit, and it's a mash of british and american...
My teachers told me that for exams like ESOL, it does not matter if you have a Welch accent or a Canadian accent, as long as you keep a pattern (i.e not changing how you pronounce words) and speaks it fluently.
I've been watching True Blood on DVD, and it struck me as odd that one of the
caption options was "Brazilian Portugese".... I spoke with a friend from Brazil, and
she told me, sure enough, there's a distinct difference of dialect. In college, I
had a classmate who was a native Spanish-speaker, but who failed the placement
test for fluency because she couldn't understand the Mexican guy who recorded
the test clips.
...and, of course, the can't English speak their own language anymore. 
Yes. Our portuguese is slightly different from european portuguese. We have some differences on how we say some words, a little with verbs (present continuous), and with spellings - all that but the cultural aspects of the language. However, the most differences comes from how we speak. Meaning, I can fully understand what they write, but sometimes their portuguese sounds uncommon. It get awhile to start understanding.
To reduce these writing differences, there was an agreement signed by both countries and some other portuguese speaking countries. At the end, these differences tried to make portuguese more unified, but it failed. Kinda complicated to explain it in english without having to teach portuguese grammar that I dont know by heart.... sorry.
Edit: I wouldnt say dialect. maybe 'idiom', since when writing or speaking we follow the same rules.