It doesn't hurt to know something of what other religions teach, if you're often around followers of those other religions. Aside from that, the more intricate details of what other religions teach are little more than academic curiosity. I agree with others that you need to be well grounded in Scripture before looking in detail at what other religions teach.
Be aware that when you're talking to someone of another faith you're not necessarily going to get very far by merely pointing out how what their faith teaches differs from what the Bible teaches. Unless someone accepts the Bible you might as well be quoting from Moby Dick. Even faiths that may notionally accept the Bible (I'm thinking primarily of Islam here) will have some form of defence mechanism to ward off teaching from the Bible they find unpalatable. I used to engage with Muslims frequently on another board and their standard line was typically that the OT got corrupted by men so God gave us the NT, and then the NT was corrupted by men so God gave us the Qu'ran. How a God sufficiently inept to prevent his word getting corrupted twice managed to work it out the third time was never made entirely clear.
Any faith that teaches that the Bible is good but their book is Bigger and Better, in whatever form of words that claim comes, will have a ready-made excuse for not accepting Scripture. It's been twisted, it's been corrupted, which is why God gave us this New, Bigger, Better book that they use and that, according to them, we should also be using. If you're in the US and dealing with Mormons that's going to be a tricky one, given a belief that Jesus left his disciples and then went to America to save the people there. They have an obvious "out" to explain why their book is more appropriate than the Bible.
Cults are even more tricky to deal with because it's more likely they won't even be given the resources that might be used to counter their faith's teachings. A classic example is the Jehovah's Witnesses and their "translation" of the opening of John's gospel that reads "the Word was with God and the Word was a God". It's a subtle change from orthodox versions but changes the very nature of Jesus Christ. I'm not a scholar of Greek, but from my understanding you can't get that out of the Greek without twisting pretty hard. I'll hazard a guess the JWs are not encouraged to compare their version to the original Greek.
