Conflicts of interest are what I try to avoid the most. Often (if you are a good natured person) you never see these coming until they are right on top of you.
I worked briefly for a company as an all around technology 'go to' person. I ran the network, I made the web sites, I developed some custom software and handled the on-call tasks. The opportunity came at a really good time for me, I was between major projects as a freelancer and needed something to plug some financial holes. I made it clear that I was not an employee, just a very part time contractor and that did have other clients, just none in the same industry.
The CEO of the company also owned a charity, which was doing good things. He asked if I'd mind helping to re-do the web site in anticipation of a large fund raiser. I wasn't really busy, it seemed like a good enough cause and favours tend to come back to you in good ways.
What I did not know is, the charity site was going to take a LOT more time than I anticipated. I didn't realize quite what they wanted until I got too far into things to pull out. If I did, there would be no way that they'd be ready for the fund raiser.
Meanwhile, stuff started really heating up at the company. I fell way behind on several things, a lot of people who were depending on commission were being let down and the CEO directed me to work exclusively on the charity stuff and asked that I not tell anyone what I was doing.
I never saw that coming. There I was, I had to explain to people why things were delayed, and here's the CEO asking me to be dishonest. There's no good way out of something like that. At this point I just realized what I walked into and I knew that no matter what I did, someone was going to get mad.
Consequently, I no longer take 'side projects', even unpaid, for whatever cause.
I believe that most productive people (who go through the bother of having a job, etc) are also generally good natured and want to follow rules. Some people, however (at least in my experience) aren't so good at realizing when they are effectively putting someone in a very compromising position.
You really do have to be careful, your work environment can go from fantastic to dreadful very quickly in these kinds of situations, and you almost never see them coming.