Crunching the numbers has always been the hard part. Taking a sighting is relatively straightforward if you have a horizon. Apps available can pull the almanac data and crunch numbers. There are way too many ways to screw that up without constant practice. I've got apps or .exe's on a number of devices -- iOS, Android and PC. They all work, the math is very mature.
I'm learning CelNav too (a bit stalled at the moment, but need to get back into it).
I don't see the utility of using apps. Seems to me that the point of CelNav these days is as a backup when everything goes to hell. Meaning that your device with the app on it will be a paperweight. GPS will be gone. Atomic clocks will be gone. So you need to me able to do the math manually. And you need a long term almanac to look up the data.
Sure, have an app to crunch the numbers while the app's host device still works, but know how to do the math manually for when the device fails. But if you're going to be depending on an app, why not just depend on GPS in the first place and forget about learning CelNav altogether? GPS is more accurate, much quicker, and far easier than CelNav.
The one thing I haven't figured out, is how to you have a long term accurate watch/timepiece that doesn't depend on outside technology and batteries? How do you verify it's accuracy and reset the time when appropriate? If you know your precise location you could use that to reset the time on your watch by working the numbers backwards. But if you don't know where you are to a precise degree, and you don't have a trustworthy time reference ... that's where I'm lost in what to do.