Jennifer wonders "if lawyers with almost-unintelligible accents ever become trial lawyers?"
The answer, sadly enough, is yes. No matter how hard we try to keep people from the Appalachians from becoming lawyers it just keeps happening. And now they even have their own law school so we're basically doomed.
Seriously though, yes people with thick accents do become trial lawyers. It's more common in larger urban areas where there are more immigrant communities but you run into it all over. I've seen guys in court with accents from the subcontinent (I won't pretend to know which accents), Arabic accents, and some African accent. Mostly, they are attorneys who have been hired to come down from DC. Strangely, all the many Spanish speaking lawyers (at least hereabouts) speak excellent English.
My feeling on this is that these lawyers get the majority of their business from people in their ethnic community who wish to have someone of their ilk represent them. After all, who hasn't had a client fire them because of race, ethnicity, sex, etc. and go hire somebody who can understand their particular needs? I know I have (picture a guy speaking with an almost comically stereotypical Italian-American accent firing his attorney because he's never been to Brooklyn).
In general, I see these guys do a fairly good job for their clients although I must admit to never having seen a jury trial by one (not surprising as juries are fairly rare in Virginia). A couple times I've heard judges ask questions along the lines of the "2 Youts" question but most of the time it's just a matter of listening a little more intensely and everything goes well.
Only one time has an accent irked me. I walked into the court and spoke with a prosecutor I had never met before. He spoke with but the slightest British accent and told me all about how he was going to convict my client. I told him we were pleading not guilty anyway. When we got to the bench he broke out into a full-blown British upperclass accent. It was either the pressure of actually arguing in front of the judge or - and I suspect this even now - it was an attempt to use anglophilia as a trial tactic. Still, I won the case so it was pretty much impossible for me to get too upset.