With climbs like El Cap, a tiny mistake could be something as simple as letting momentum carry you a few degrees too far, losing your focus for an instant, or even losing strength. Climbing is a cross between chess, long distance running and gymnastics and to free solo something like El Cap, you need to be world class at all of those...simultaneously.
Several years ago, when I had a total of three hours of climbing experience (one hour in a classroom and two hours on an indoor wall), I made a mistake ice climbing that could have been fatal if I had not been properly roped in. I was incredibly inexperienced, got incredibly scared and started gripping onto my tools for dear life. I was so scared that I put all of my strength into my grip. My forearms spasmed and I lost my grip. I was an ugly climber, so my belay partner had given me a little too much slack, so I fell about six or seven feet, thus leaving a very experienced climber's very expensive tools in an ice wall several feet above me. Rather than get lowered and try to recover his tools the proper way, I decided to use crampons and my gloved hands to climb the ice like I would climb a rock. It was an incredibly sunny day, so the waterfall was a little wet and that was likely the most miserable seven feet that I have ever climbed.
In retrospect, it's a funny story about a noob getting scared and I had to buy several rounds of beer when we got back to civilization. But, that's an example of losing focus and doing something incredibly foolish that could have had tragic consequences.
The particular route Honnold climbed (Freerider) is hardly "cutting edge" (at 5.13-, it is roughly eight or nine grade levels below the absolute hardest rock climbs in the world), but the most difficult section (the "crux" in climbing jargon) is notoriously insecure, meaning that even skilled climbers find the movement difficult. Honnold himself spent time on the route on a rope learning this sequence (and others).
I seem to recall him saying in it one of the big risks is suddenly being overcome with fear or vertigo from the height.
Granted, I'm a mediocre climber (can lead 10c/d), but falling every once and a while is pretty common for most of us.
The rock can break off ("chossy" climbs, Pinnacles is notorious for this), but that's a less common occurrence than Hollywood would lead one to believe.
Heck, a few years ago, a 2000 ton slab of rock fell off of Half Dome, which is a famous granite dome in Yosemite. I can't find the article now (of course), but I read a great article about how rock expands and contracts with the heat of the sun, water gets into cracks and plates will break off.
This article is okay, though it isn't the one that I'm thinking of. If I can the correct article, I'll edit this answer.
http://www.livescience.com/51490-yosemite-half-dome-rock-fal...
10% of El Cap accidents are falling objects http://www.climbingyosemite.com/portfolio/danger-zones-nose/
Rock fall meanwhile is dangerous to all climbers, whether or not they're using ropes. Sure, it's more dangerous to a solo climber - you might get lucky and just get knocked out, something a rope can save you from - but we're talking about a moderate risk vs. high risk comparison, not zero-risk to high risk. That 2000 ton slab you gave isn't a very good example, because something that big has a pretty good chance of killing you rope or not.
FWIW, I do a lot of cave exploration, and in caves the "already broken off" effect is a very powerful one. Virgin passage that's never been explored before can be a very scary place to be because everything can be loose and ready to fall. This is particularly true in areas that undergo freeze-thaw cycles, such as upper parts of alpine caves - I've been in places where every single bit of rock, including the ceiling, is heavily fractured due to frost. Breakdown piles are also a big problem - they're huge piles of rocks and boulders, generally due to ceilings gradually collapsing, and you have to be really careful around ones that haven't been visited frequently because pretty much anything you stand on could be unstable. Lots of cavers have been trapped in breakdown piles that shifted unexpectedly.
The underlying cause of this problem in caves is simple: caves can be very static environments with no weather, increasing the chances that the force you exert on a rock will be the largest force it has ever experienced in that position.
It occurs to me that this phenomenon will also be a big risk factor in lunar exploration, if people ever go back up there.
Oh, is http://idlewords.com/2007/04/the_alameda_weehawken_burrito_t... yours? That's basically my favorite blog post ever.
For example, I've personally done quite a bit of what's actually free soloing in cave exploration, but that style of climbing is done in confined spaces with rock on every side. You're much less dependent on individual holds as you'll usually be supporting yourself by pushing against the rock with your whole body, so it's a lot safer than most free soloing - even if you do fall you have a good chance of self arresting by, and if you can't you can at least slow your fall significantly and just slide to the bottom.
I was highlighting the sudden surprises that tend to catch a climber off-guard. If someone is climbing on wet sandstone, they should already be cognisant that it may crumble. (They should also avoid climbing it when wet so that they don't break holds, but that's another topic on stewardship.)
A doctor from our local hospital died from, as far as we can tell, exactly this while climbing Discovery Wall. He was an excellent climber, and was using appropriate gear. He just was in the wrong place at the wrong time, and his safety equipment wasn't enough.