This is possibly one of the best examples why a large group of musicians needs a conducter, whether its an orchestra, a large choir, a big band, a show band, a marching band, whatever.
If you look at the score for this peice there are so many bars of odd time signatures, and a large amount of rubato passages. To play this in a full string orchestra, there needs to be someone showing where each beat falls, showing where to bring notes off, showing where the dynamics fall, everything. The conductor, should by nature know every note in that piece, by heart, so if someone is wrong he'll hear it.
I play in a big band, and when we've rehearsed without the MD its incredibly hard, unless someone is able to call of notes and each section leader knows what their section is supposed to be doing. Having each little section reherased so every note is spot on is one of the biggest parts of conducting, interpreting the written music into something that is heard and felt, such as the Barber Op. 11. If one person is out of tune, the conductor should be able to tell whether the player is sharp or flat, so make sure everyone is sounding their best.
All of this is practically impossible without a conductor, or director.
watch the section from about 6:30, until about 7:50, and you'll understand why a conductor is needed.