The biggest problem I have riding is keeping my feet correctly placed on the pedals. If they turn while riding, repositioning them often causes me to lose control or fall. Last night I fell heavily backwards because my foot got trapped on the pedal, I couldn’t put it on the ground fast enough, and fell backwards onto my back. Fortunately I fell to the side onto grass. But it makes me wonder if there’s a better way to do it. In a lot of videos of good riders, the arch of the foot is on the pedal, instead of the ball of the foot, like is recommended for regular bikes. Also, do I want real sticky shoe soles or metal pedals for the unicycle, instead of plastic?
This is a common problem for newer riders. Try to put more weight in the saddle and less weight on the pedals. Eventually, you will get to a point where you can comfortably reposition your feet without losing control. It takes time and practice. Arch versus ball is debatable I guess, until you do big drops. Then landing on the ball may break your ankles.
oh and Use flat plastic pedals for learning…
I agree with MadFurai: this comes easier with more riding experience. The best ‘window’ for foot placement adjustment is if the pedal is on the rise because then you have the least pressure on it anyway. You may want to try and bring your knee somewhat outward, also bend your ankle outward. That will tilt your foot at a sideways angle on the pedal, with less contact area, which is a better starting point for adjustments that full contact. With experience you will be able to lift your foot completely off the pedal and re-place it in a better position, without even thinking about it, even with pinned pedals and sticky soles. For now though, stick with less sticky soles or you might be stuck 
Are you riding indoors or out. For outdoor riding you’re generally better off with the metal pedals with short spikes on (and, if it’s wet, they’re essential).
Shoes are important- I prefer trainers with relatively thin soles- it’s worth trying different types out till you find what’s best for you. Try pumps/plimsoles as well.
I recently went for a ride with a different type of shoe, and had difficulties (incidently, I’ve been riding outdoor unicycles for over ten years).
My advice concerning shifting your feet around when they’re on the pedals (re-adjusting them) is to be wary, and, if in any doubt whatsoever, dismount, and start again.
One of my worst UPDs happened on a 29-er when my left foot got slightly dislodged and I tried to work it back into place: learnt a lesson there- if that happens again, I’ll just dismount.
In contrast, I’m very comfortable re-adjusting my right foot. I guess it’s cos it’s the last foot I put on the pedals when I mount, so I’ve had a lot more practice shifting it around: whereas my left foot is the first foot on the pedal, so, from the mount, it’s always placed perfectly, and, the only time it gets moved is on the very rare occasions it shifts during the ride.
(I guess that’s a good incentive to practice mounting with both feet equally, but I never got round to that- too busy enjoying riding the thing:) )
Overall, I’d say, ‘safety first’: if in doubt, just dismount. Soem the worst UPDs are those in which a foot gets caught on the pedal and can’t be put on the ground, as you found out: falling backwards on your back is not a good thing, and, if you get in the mindset of getting off the unicycle as soon as things start to feel overly dodgy, you can save yourself from most bad UPDs.
With the right soles and spiked metal pedals, your feet are far less likely to slip than with plastic smooth pedals- the counterside is that, if they do slip, it’s harder to reposition them (due to the spikes/friction), so, again, if metal spiked pedals are new to you, definitly get into the habit of dismounting whenyour feet slip, until you have enough experience to tell whether it’s feasable to reposition them on-the-fly.
Additionally, while I’m not big on learning tricks on the uni, I did master idling, and, that is very useful for readjusting the foot.
i.e. go into a idle, and, it’s fairly straightforward to shift the top foot around as it’s at the top of the stroke with relatively little weight on it- obviously make sure you’re very comfortable with idling before you try it.
I find that works very well for the right foot, and, had I put in the effort to learn idling on both sides, I’d no doubt say the same about the left foot
The other benefit, is that with a good solid idle, if you mount using the ‘rollback mount’, and your mounting foot isn’t on perfectly, you can immediately go into idling, and reposition it.
+1
I also have problems w/ my feet easily slipping out of ideal position and then sometimes off the pedals. Extra grippy metal pedals (JC’s w/ 12 mm screws) solved most of the slipping, but as MadFuria said it’s harder to shift, worth it IMO.
Riding along and lifting one foot (ie the left) at the top of the stroke a tiny bit every once in a while, and then every revolution, while staying relatively smooth really helped w/ my ability to adjust my feet. As Bill said if you keep at this eventually you will be able to take a foot off for a whole revolution and eventually as many as you want.
You might also try different pedals. I have a metal set with pins (super grippy), the Nimbus nylon pedals with metal pins (stock on nimbus Munis), and the cheap all plastic ones. Overall I think the Nimbus nylon ones are the best compromise of grip and ability to change foot positions. However, as my Muni skills improve (been riding 2 years now), I’m beginning to notice that my feet are slipping more as I tackle tough terrain with more speed. I’m probably going to go with the all metal pedals soon and give them another try.
As others have noted, the shoe makes a big difference to. I prefer a Vanns style skate shoe with a smooth rubber sole.
Learning one footed riding is far more useful for readjusting the foot 
That’s something I’m working on at the moment, and I definitely find it fairly straightforward to adjust the foot I’m trying to take off - should really do a bit more practice on the other side, as if nothing else it might make adjusting that foot a lot easier.
Yeah, some people preffer shoes w/ flat soles (5:10’s are popular, super grippy sole), but I preffer shoes w/ a definate heel.