I'm more like Seven in that the end of that one episode where her and Janeway eventually end up saving Voyager from 'sploding and then Janeway was all 'bah TIME TRAVEL' and Seven was all 'time to explain now!' and then get shut down.
I get shut down a lot when I try to explain things.
Also, thank GOD for Chakotay screwing up his almost relationship with Janeway >:3
The thing is, with infinite universes, you go back and change the past and a new timeline is formed, right? So your old timeline, which you belong to, doesn't change. But you are now in the NEW timeline and, for your purposes, you solved your old timeline issues. However, it's rather like a suicide mission in that you prime cannot go back to the future because the new you already exists there and won't have to go back in time because this is an entirely different timeline with entirely different results.
ie, in Mobius, Daniel determines that a ZPM was on Earth back when Ra was ruling it. So they take the timeship back four or six thousand years (can't remember which) to go steal the ZPM (something that Sam eventually agrees with because the goa'uld don't use ZPMs and there's no evidence of it on Earth at the present time).
So they go back in time, steal the ZPM and... have their ship captured and thus can no longer go forward in time with their ZPM. So a new timeline is formed and Sam was all 'oh hell no!' and they record a message to their futureselves informing them that if the future isn't how it should be, go back and fix it kthxbai.
In the new timeline, Jack and Teal'c get sick of not fighting the goa'uld and start up the rebellion that kicked Ra off of Earth a bazillion years ago. Buuut that was premature and then Jack, Sam and Teal'c all get killed and Ra DOES leave Earth... but takes the Stargate with him.
So in the new timeline, the one without the Stargate, Sam isn't a kickass scientist/soldier - instead, she's rather shy and meek and wears awful clothing. Daniel, since his pyramids as a landing site for aliens theory wasn't proved, ends up teaching English to immigrants. Jack, for some reason, doesn't commit suicide and is a boat captain who spends his days fishing. Teal'c is still in the service of Apophis.
All of this simply because there Is No Stargate In Egypt.
Long story short? No paradox. Just a new timeline.
However, also in Stargate, there were earlier episodes in which there ARE paradoxes. In 1969, SG-1 accidentally gets sent back to 1969 because of a solar flare... but, before that, General Hammond gives Sam a note that says when solar flares in 1969 are going to happen so they can get back to... 98?... because they encountered him in 1969 and told him what was up. Then there's also the 2010 and 2001 episodes.
Conclusion? Janus' timeship fixed the paradox problem by using the parallel timeline thing but the Stargate doesn't have that safety protocol.
tl;dr and away!