What are the odds Bitfinex is not AML/KYC compliant for a significant share of its transactions?

Medium to high probability. But chances are the company is fixing that. Plugging the holes, fixing the short-comings, etc. There is an extremely high-probability that they have had serious infraction when it comes to their compliance program.

Whilst it is good that they are fixing it - the problem is, past infractions are still past infractions and any regulator can pounce on them.

The question is - how good will Bitfinex be to cover them up.