I am a little confused as to the second thing with white spots on it... Nudibranchs are pretty impossible to crush or trap, as their shells are small, flexible, and totally encompassed within the body, so I wouldn't worry much about that. I just found two sea cucumbers in a clients tank that I never put in there and they didn't know about, and I had been caring for that tank for two years when we found them. Squishy stuff can usually make it out.
Nudibranchs are notoriously short-lived, and are usually very VERY particular about their prey items (one species, one prey item), so they are almost always a bad idea to stock since they are doomed when they clear your tank out. Pretty much all nudibranchs bioaccumulate toxic compounds to deter predation, and I have heard these can unleash hell in your tank when they die and foul as well. I have never had the beans to stock them in my tanks, though I will pick up a Navanax sp. soon since I have red planaria blooming in my 30g.
I am not sure what species you have, but I can only imagine that when it runs out of appies it is coming for your coral. Keep your eyes peeled.