By virtue of where the seat of Government is located, the Federal District Court in DC gets more than its fair share of high profile cases. The problem with this is that the cases are often political and the available jury pool is heavily biased in favor of Democrats. DC has NEVER voted for a Republican Presidential candidate. Never. Not even in 1984 when every state other than Minnesota voted for Reagan. Even in the face of a national landslide, 85% of DC voters picked Mondale. With a potential jury pool like THAT, how can a high-profile Republican in a very partisan case even hope for a fair trial? Now, I'll admit that the same might be true for a high profile Democrat on trial in Utah or Mississippi (though no state is as overwhelmingly Republican as DC is reliably Democrat). The problem there, however, is that high profile Democrats don't go on trial in Utah or Mississippi.
It would be easy to suggest that such cases should somehow be handled with a nationally selected jury pool. I don't think that's practical. It probably also wouldn't be constitutional either. In fact, I'm sure it wouldn't be. This is one of those problems that doesn't have an easy answer. The only way Republicans are ever going to have a level playing field among a DC jury is by making substantial in-roads in the Black community and among civilian government employees. In the long term, I'm hopeful we may achieve the former but I doubt we will ever see the latter.