I think one of the most common worries from people preparing to tackle the Continental Divide Trail (CDT) is navigation. Recently there was a post on the CDT2017 Facebook group with one hiker asking if you could wing it, or if maps were necessary.
The short answer is, maps are necessary. You can wing it with regards to resupplying, and deciding what altnerate rounds you want to take, but you cannot navigate the trail without additional resources.
Day one, heading north I came across this fork; does the trail go left, or right? Honestly, I'm not even sure, I went right but I had to just cross-country my way out of the area.
No tread on this part of the trail, just going from CDT signpost to CDT signpost. If you look closely in the middle of the picture near the horizon there is a white spot, that is the next CDT sign I'm moving towards. Sometimes these were nice a close such as in this picture, many times you wouldn't see the post until you were practically on top of it (or literally if it had been blown over).
Without accessing some map you'd have a hard time trying to make your way through these areas without good trail, but even with trail you'll have some issues.
This I think is a great example of how the CDT might detour from the obvious route. There is the clearly defined trail on the right half of the picture, that is the CDT heading continuing north. The same clearly defined trail also continued south behind me taking this picture, but the CDT heading for a south bound hiker make a quick 180 turn onto that very faint trail to the left (which switchbacks up the mountain). I actually missed this turn even though I knew it was coming and took this picture while backtracking. Without a map to know that such a turn was coming you would almost certainly miss it. There was no marking, no sign post, nothing to indicate the trail was even through when walking the CDT southbound.
These are just a few examples of the type of issues you'll encounter hiking the CDT. Though its nothing terribly difficultif you have appropiate information to reference, trying to wing it with regards to navigation is a bad idea.