Of course, none of us can actually verify every fact we hold as true. We simply do not have the time, and even if we did, we do not have the expertise. At some point, one must resort to argumentum ad verecundiam, at least in our own minds. Of course, the argument from authority primarily deals with citing an "expert" for something outside their area of expertise. Still, two physicists may disagree on a matter of physics. Argumentum ad populum is commonly used to resolve this, but that is also fallacious. But what choice do you have? Even if you happen to be a physicist, there are countless other areas of expertise you have no qualifications to judge. We are social beings, and our incredible advancement means none of us know everything: we must resort to trust, at some point.
Sometimes it is not obvious to us whom to trust when looking at competing hypotheses. It is at this point, the liberal use of certain philosophical razors can help us. A philosophical razor helps us quickly eliminate unlikely scenarios. It's of note that no such razor is universally correct - but in the absence of personal expertise and time to investigate, they will steer you away from bad choices in facts, most of the time. The most common of these is Occam's Razor: Choose the hypothesis with the fewest assumptions. There are many others, though.
My personal favorites:
Alder's Razor: If something cannot be settled by experiment or observation, then it is not worthy of debate. (Also known as "Newton's Flaming Laser Sword" - this gets rid of so many discussions that are simply not worth having or considering.)
Hanlon's Razor: Never attribute to malice that which can be adequately explained by stupidity. (This gets rid of most hypotheses that require conspiracy. There is some difficulty in sourcing this commonly cited razor, it may actually be Heinlein's Razor: Do not attribute villainy to conditions simply resulting from stupidity.)
Hitchens' Razor: That which can be asserted without evidence can be dismissed without evidence. (I hope this one catches on. Hitchens was a visionary.)
Popper's Principle: For a theory to be considered, it must be falsifiable. (This is the best way of dealing with superstition. "What would, in your estimation, prove your idea wrong?" If your answer is "nothing," then you're almost certainly wrong.)
Run every idea everyone ever presents you through these razors. If an idea conflicts with one, well, consider if it's worth investigating further. Maybe you can find proof of the assumptions and Occam's Razor no longer applies. Maybe you can think of an experiment or observation to help prove it. Occasionally there actually is malice. Find evidence of it. Maybe the person making the assertion hasn't looked hard enough to find evidence yet. But probably - you can simply move on to another idea that has been better thought out.