One of the dangers of mentoring someone on your team is that you can easily be perceived as biased, and the protege as the 'teachers pet'. In fact those are pretty close to the truth! It just doesn't work to mentor someone that you don't believe in and because of that, you'll give them more of your time, and put more thought into the assignments they get. Does that mean you shouldn't mentor one of your own? Ideally I'd say yes, but practically speaking most organizations aren't big enough to support anything else. That's one of the reasons I suggest putting in place a full coaching and professional development methodology, it helps those that for whatever reason aren't a good fit as a protege (it's all about chemistry) and gives you some cover (just being honest here) so that you're not seen as neglecting your team. In practice you should work things so that any unusual time devoted to mentoring is in addition to the proteges standard schedule.
What about mentoring someone on another team in the company? Again, you have to be careful about perception, and in particular about how you discuss the manager with the protege and vice versa. Undercutting another manager is a recipe for pain, but sometimes the reason you're mentoring is because they haven't learned or don't care to participate in mentoring (or being a good manager/leader!). I think it works best when you have a good relationship with the manager, because you can share some - not all - of how the mentoring is going with the hopes of steering the protege into growth situations.
The easiest scenario in terms of conflict is someone from outside the company, the downside is that you only get their side of things in most cases, you're not seeing them handle things at work. Easiest, and my favorite scenario.