Why didn't Eris interfere with Sinbad's return voyage? If she did anything to FORCE his claim to be a lie, it'd go against that deal she made with him. He didn't know her claim of him lying wasn't applicable until the moment of truth. But either way, actually trying to force his hand against his will would be breaking her word which she couldn't do.
Following on the above, the fact that if gods swear an oath they are 'bound for all eternity' to keep it, while well set-up earlier in the film, seems to act as something of a Deus ex Machina to save the day at the end. Except that, all historical/mythical changes in the film aside, this actually seems like a very clear reference to the Greek deities' swearing on the waters of the River Styx (and indeed, being unable to break such an oath once sworn). The animators merely used the 'X of light' Eris makes on her shoulder (since she "doesn't have a heart") as a visual shorthand or explanation for this.
Sinbad loves the sea. Marina's names mean "sea". A possible romantic foreshadowing of them falling in love with each other.
Sinbad's harsh treatment towards Marina, especially his Stay in the Kitchen lines directed at her, makes him out to be a chauvinistic jerk. Then, Sinbad confesses to Marina that she is the love of his life, from the very first moment he saw her. The moment she came to be arranged to marry Proteus. So, his earlier actions make more sense when you realize that his said actions was because he was trying to push her away from him, so he wouldn't fall more in love with her than he already was.
That begs the question of what the other gods were doing while Eris was meddling in mortal affairs.
Well, the gods tend to go out of their way to AVOID Eris in the first place (Apple of Discord, anyone?) and then it's the fact that most of them don't get involved in humans affairs unless it's related directly to their own interests. It could also be that they already knew what was bound to happen.