I'll take a stab although I don't know that much (since you're asking a question about CT design I'm assuming you probably know a lot more than me).
I'm guessing that the biggest phase error comes from the excitation current, which is approx 90 degrees lagging load current (assuming resistive burden) resulting in phase shift (no phase shift if you're driving an inductive burden).
I'm guessing that leakage reactance would be the next most important factor.
How to minimize excitation current: increase the number of turns; use higher-mu iron, provide bigger core cross section.
How to minimize leakage reactance: reduce number of turns, keep the gap between the secondary turns and the primary conductor as small as possible.
