With 2 stroke oils... there isn't a "Standard" like with car engine oils. And on top of that... there are several different catigories of 2-stroke oils. Each having a different additives package. Because of this... YES... you can have unpredictable issues when mixing. I've seen everything from jello, to "Stuff" just falling out of solution. Both are very bad for your engine.
Every "New to me" PWC gets a full oil system flush and service. That way, I know EXACTLY whats in the tank.
With that said.... MOST TC-w3 type oils can mix, as they have a similar additives pack. (It's the fish safe oil) I still generally say to not mix synth and dino oils together. But under no circumstances should you EVER use a TC-w3 oil in a Seadoo PWC.
****EDIT****
I just saw your skis in your name. I know Yamaha says TC-w3 oils are ok... but they LIE !!! lol. If you want that GP1200 to live a much longer life, feed it only a synthetic API-tc, or Jaso-Fc oil.