I find it's this kind of answers that make scientific explanations so hard.
"Blindly trusting scientists because they're perceived experts, have advanced degrees or are in agreement in large numbers has historically been an unreliable way to judge whether or not something is in fact true."
First of all: if they have an advanced degree in a subject such as medicine than I think they deserve that you drop your hidden insinuations in the adjective "perceived". They studied the topic, they did at least 7 years and maybe more. Other things being equal, isn't that something that matter? Or put it another way: if random "guru" tells me one thing and a scientist the other, I'll probably lean more toward what the scientist said, though I won't feel I am in a position to be sure he is right (but if I had to bet, I'd say he is more likely to be).
Second annoying word was your adverb "blindly". There is nothing blind in following the scientific consensus. The consensus in science is not formed by a group of guys rolling dices. A good scientist is a sceptic, and if many scientist agree that (say) we evolved from monkeys then I think they have a pretty good argument. They are not saying: "trust us because we are the wise men", they say: "trust us because we've done experiments and so far this is our best theory... if you can disprove it, then try".
Third the large number of historical cases you refer to... large numbers? Seriously? Give me a percentage: what are we talking about? 5%? 1%? 0.01%? Sure, science has its up and downs, and sure there are Kuhnian paradigm shifts from time to time. Boltzmann found strong opposition, as did other famous scientist: but those are the exception, not the rule. Just because these exceptions are so rare that they end up known by everyone, doesn't mean that they are in any "large number" what so ever. Again, give me a percentage.
Finally scientist do NOT dismiss all opposing viewpoints because they don't fit a model. Sure, a model that goes completely against 200 years of science will find opposition, but for good reason: that theory had proved itself for so long after all! At the same time when a scientist proves something people seem they can immediately come up with a random objection... which of course the scientist had already accounted for (and then some).
There are a few exceptions. I think most scientist will dismiss anyone who says they built a perpetual machine... but thank God they do. I don't want to think how much scientist time has been lost on a random guy coming up with a wacky model: scientist are not there to prove _your_ theories. If you want you try and prove it yourself! If you do and you can back up your assertions with data, scientist will listen.
One last point. No, being smarter is not enough, but it should mean something. I mean, just look at evolution: scientist may spend a few years to properly show and back up their assertions against one random opposition, and it takes like 1 day for the opposition to slightly modify their model to take into account that. That's not how you do science, and if you feel every scientist has to listen to anyone coming up with any theory and try to spend maybe several hours explaining where it is wrong, and maybe filling up all the holes in their knowledge, then I think you are deeply mistaken. You want that? Then pay for someone to do it: to be a scientist is a job!