Ironically, the amount of pressure from the top involved in this (and related) cases caused several prosecutions of sexual misconduct in the military to be dismissed. You read that right. There's a doctrine called "unlawful command influence" where, if the posture of the Commander on Chief on down suggests that there is a "right verdict" independent of the facts, then the military courts should dismiss cases rather than having military officers be, essentially, ordered to convict.
A certain US president who is a Constitutional law scholar has run into this at least three times and professes to be really surprised every time it happens.
To be fair, the Uniform Code of Military Justice is wholly separate from the Constitution and the modern form (including the unlawful command influence clause[1]) has only really existed since 1950.
He probably should have been more wary after commenting on the Chelsea Manning case, but it's worth noting that there have been many judges who haven't dismissed cases after his remarks, so at the very least the propriety of his statement (which was fairly tame and limited to calling for discharge once convicted) is debatable.
While that's not good, it's very different thing. Those two examples were of normal, civilian courts, proceeding of an independent judiciary; a President or Prime Minister has the "power of the bully pulpit", but no formal power. Our minimalist Constitution goes so far as to say Federal judge compensation "shall not be diminished during their Continuance in Office", i.e. the other branches of government can't dock their pay.
In military courts, the judges and jury are in the chain of command, so as patio11 put it, "the military courts should dismiss cases rather than having military officers be, essentially, ordered to convict." Hence the formal name "unlawful command influence".
A certain US president who is a Constitutional law scholar has run into this at least three times and professes to be really surprised every time it happens.
see generally: http://www.nytimes.com/2013/07/14/us/obama-remark-is-complic...