The interwinding capacitance of isolation transformers can be significant - you mentioned just over 1nF - which at mains frequencies is nothing. However, if you have HF noise and interference on the mains, that will capacitively couple over to the secondary and appear as a common mode voltage on the Live and Neutral with respect to mains earth. If you're probing your circuit directly, with your scope chassis grounded, you may find this upsets your measurements due to this common mode current draining through your scope probe's ground lead.
As Dave mentioned, an electrostatic screen between the primary and secondary almost eliminates interwinding capacitance. This is simply a layer of foil, connected to mains earth, between primary and secondary that is wound in such a way that is does not form a shorted turn, but gives complete coverage of the primary-secondary insulation. While this almost eliminates coupling between primary and secondary, if you have common mode noise on your mains earth this can still couple from the screen into the transformer secondary which will once again drain through your scope's ground. Again, it might not be a problem unless you're making absolutely critical measurements.
I mentioned that 1nF at mains frequencies is 'nothing' but this is not entirely the case. At 50Hz, 1250pF has a resistance of about 2.5M. If you connect your scope probe tip directly to the live or neutral output of the transformer with the ground unconnected, you'll see about 0.8x your mains voltage on the scope trace because this 2.5M becomes the top end of a potential divider to the mains with the bottom end being your scope's 10M input impedance to earth. In other words, it'll look like the isolation transformer isn't doing anything.
In either case, if you're making precision measurements on a mains-connected circuit, it's a good idea to use a heavy mains filter at the input of the isolation transformer to attenuate any HF before it has a chance to couple through the transformer. Better still, combine this with a proper, high quality, high bandwidth differential probe. While the CMRR of even the best differential probe is not infinite, it still breaks any earth loops formed either directly (if your DUT is earthed) or indirectly (through interwinding capacitance to the primary, or through coupling from the electrostatic screen).