Internet Monk has a post on how even conservative, inerrancy-believing preachers often end up preaching from Song of Solomon as though it was a manual on marriage and sex. The problem isn't that what they're teaching on the latter is wrong, it's that it's not what Song of Solomon is actually getting at. It's not good exegesis. I can identify somewhat with this, having heard more than one sermon where my internal response was "what you're teaching is fine, it just doesn't say that in the passage you're preaching from".
Actually, I think he's hearing in a scenario where it's much more obvious something that goes on with a lot of scripture. Even the intent to be correct theologically can be a distraction at times. E.g. I've begun to find myself getting irritated at the way if a passage contains terms like 'elect' or 'predestination', you can almost be sure the person 'exegeting' it will end up hammering on one side or the other of the Calvinist vs Arminian argument. But sometimes what is being talked about in the passage has nothing to do with that argument, and if you insist on looking at it from the perspective of that argument, you're going to miss what's being said. For example, what Paul's trying to get across in Rom 8:28-30 is the same whether you look at it from a Calvinist or an Arminian viewpoint. I get the impression, though, that few people actually follow Paul's logic in this passage, either because they stop at verse 28 ('God works all things for good'), or because the term 'predestination' in verse 29 puts them into Calvinist vs Arminian mode. (I guess this means I need at some point to post what I think that logic is).
Part of the problem (and at this point, I'll admit that I'm possibly dropping into my own agenda, as this is an issue I've seen God make an emphasis in my life) is that the vast majority of people just don't listen very well (and exegesis is essentially (or ought to be) good listening formalized). Generally, we listen, not to accurately understand what the other person is trying to get across, but to gauge how the other person's words fit into our own mental framework. Good listening requires acknowledging that the other person may be working from a different mental framework, viewpoint, or background than ours. A good listener may very well disagree with that other framework or viewpoint, or regard it as invalid, but will agree to understand that that is where the other person is coming from. Good listening requires learning to recognize the clues that indicate that there are framework, viewpoint, background or terminological differences between the speaker and the listener, and taking it into consideration (which at times includes recognizing that you don't yet understand what the speaker is trying to get across). And Good listening is, alas, in short supply.
If you haven't picked up the above good listening skills, I wonder if you're really prepared to do good exegesis of scripture. If you can't listen to people, particularly people who have significant differences from you, how prepared are you to listen to the God who tells us "My thoughts are not your thoughts, nor are your ways my ways". Develop these skills now with people from whom you can get feedback, so you can figure out where your listening skills tend to go wrong and correct it (and my experience is that developing good listening skills generally starts with making lots of mistakes and figuring out where you went wrong. It's also how you figure out how to detect the clues that tell you there are differences between how you and the speaker see things). When exegeting scripture, you don't have that kind of feedback available.
C. S. Lewis suggested a pre-ordination exam testing a candidate's ability to translate the theology he's learned into ordinary language. I'd suggest that in order to be able to do that, one of the earliest courses in seminary should be a class on developing good listening skills. This should be a prerequisite to theology classes, but note that these skills are also going to be very valuable for things like counseling.