I am a natural skeptic, for the most part. Skepticism is a long forgotten virtue for humanity and it is often associated with shame. I believe the opposite and I tend to try and apply skepticism whenever I hear about "scientific" studies and many other things reported to me by strangers with microphones or associates of mine.
There are people who would find my skepticism as a direct conflict to my professed faith in Jesus as the only way to true salvation. Unbelief is often considered to be a problem within the Christian church and atheists and agnostics are usually shunned by the more fanatical believers. But I don't look at having doubts as necessarily a bad thing.
To me, doubt only builds faith and solidifies your belief in what you know by faith. In your doubt, you can investigate for yourself and come to your own conclusions. My own doubt has caused to investigate the nature of my own faith and the Truth further.
Beyond that, I often find myself skeptical of all media reports, though some more than others. The New York Times, for example, has lost pretty much all credibility with me after the Jayson Blair scandal. It's no wonder that they are struggling for newspaper sales (and ads with slogans like "Sunday was made for the New York Times," don't help much either). Other news organizations I give little credit too because they too tend to distort facts or jump on stories without doing fact checking.
Beyond just the news media, skepticism acts as a natural defense to succumbing to gossip. Gossip is vile and always leads to problems. Office gossip can severely hamper business as well as breed unnecessary mistrust among co-workers.
Skepticism is a natural ally of scientific study. Without it, how can true science ever be exposed. Opponents to evolution are often lambasted and condemned by the larger scientific community, even though, in many cases, they are bringing legitimate questions to the table. More often than not, these are not Bible-thumping backwoods hicks, as usually portrayed by Hollywood, but agnostic, rational men and women who merely question a very old notion of how we came to be.
While there is a certain to which you can be skeptical, there is always a limit. After all, too much skepticism can turn you into a paranoid lunatic. Trust is always a part of human interaction in varying degrees. You cannot be 100% skeptical of your spouse's actions, especially the ones you don't see, otherwise the relationship will break down. When you exchange money for something or sell something for money, you enter into a certain level of trust as a consumer or seller.
But there needs to be a healthy balance between the two. Trust and skepticism can really mess you up if you practice one without the other. Like many things in life, it is difficult to gage such things. It really comes down to having prudence. With that, you should be able to navigate through the messy world we live in and trust where appropriate and be skeptical when appropriate.
But any skepticism I express toward Christian leaders is to be understood as me being careful not to follow fools into oblivion. A church congregation has a responsibility not to blindly follow the word of a preacher but to listen and ensure that what he or she is preaching in-sync with God's Word. Likewise, a scientist has to make sure that others within his or her field of study are doing what adheres to scientific principles and natural law. The thing is, everyone has an agenda. And most of the time, you'll find that this agenda is more selfish than you may realize.