In the case of OFDM modulation, if the carrier frequency is slightly off then how does that effect the constellation diagram ?
Is there some general rule how it will change (such as rotate) ?
Or is it more or less arbitrary ?
so let's act as if we had only one active subcarrier "at a time", just to ignore interference between the different subcarriers.
The frequency offset in time domain means a time offset in frequency domain, and probably a fractional one at that. Since that offset is constant for each carrier, the resulting sample stream (i.e. the output of your DFT) is simply shifted in time.
Now comes two things:
A frequency offset usually means that your sampling rates don't match perfectly, either. In any case, this means you're losing orthogonality of the OFDM subcarriers – which is why OFDM synchronizers need to be more accurate than (non-sinc-shaped) filterbank multicarrier systems, simply because each DFT bin "sees" energy of its adjacent, slightly shifted, neighbor.
That's why OFDM systems typically make use of a proper preamble – if you enjoy reading classics, go for Schmidl and Cox' Robust frequency and timing synchronization for OFDM (Google tells me you can get the PDF from here) – in fact, that paper goes from understanding how to timing-synchronize an OFDM system to fixing the carrier offset (because they are so closely linked together).