Now this question is by no means an attack on any conductor or orchestra, nor Prokofiev himself, but why does it seem that it's hard for everyone to get right into time with one another with this piece? In literally every recording and performance I've heard the timing is off, sometimes just barely, sometimes quite obviously. This video shows what I'm getting at, and particularly shows how the different registers of the brass section seem to be out of time with one another. Still, once everything gets going things click together, which leads me to believe it's just tricky timing. I'd really like a more professional answer beyond my own speculation.
The score is here imslp.org/wiki/Special:ImagefromIndex/35364 The dance is at page 145 (131 in the pdf)
"the different registers of the brass section seem to be out of time with one another."
Low brass (f.e. tubas) tends to get the 1 and 3; higher brass (f.e. cornet) gets the 2 and 4 "afterbeat". This is in iteself not special or odd.
When I hear this piece, also in the recording you posted, I can simply count 1, 2, 3, 4, and the low brass is on 1 and 3. Does that work for you?
What might be putting you off is that in this recording, the first 2 beats start off a bit slower then the remainder. Perhaps the expectation of a slower tempo unsettles you?
You are right. The low brass (at beats 1 and 3) seems to start at a tempo that is slightly faster than the low strings that should answer at beats 2 and 4. It's sounds more like the strings answer at "2-and" and "4-and" in the first measure. They are a bit closer at second measure, and when the rest come in third measure, everything is on track. I think part of the problem is that the conductor "jumps in" when starting without any indication of the tempo.