To add to Montanero's post, estimating the distance travelled is the most difficult thing to do IME.
I have done a fair bit of navigating solely by map & compass before the GPS days, and I still do it occasionally just to stay in shape. It can be done with very good precision as long as you're absolutely familiar with the basic concepts of land navigation.
Even in difficult, unknown terrain with short lines of sight I have been able to keep track of my position pretty well, being able to find my way to some particular landmark or (even more importantly!) finding the car at the end of the trip, which is a very small target and missed easily. But it is not for the faint of heart and certainly not something that I would recommend to someone without at least a modicum of field experience.
In theory, land navigation by map & compass is not that complicated. But dead reckoning becomes difficult when you're tired or if something unexpected throws you off balance. Fatigue is a major factor IMO, it could temporarily degrade your mental faculties by a large margin without even realizing. On one particularly scary occasion (in hilly backcountry and deep snow on top of it all) I reached the point where I wasn't sure any longer if the red end of my compass needle was supposed to point north or south.
Stuff happens and if you find yourself in a situation like that you really need to STOP immediately and pull yourself together before things spin out of control.
From what I've learned on my treks, people almost always overestimate the distance covered in a given period of time. More so in hard terrain. Ranger beads can be very helpful. If you are with a group it's a good idea to have at least two people performing a pace count just in case the designated leader happens to lose track of the count for whatever reason. Also, check your current position regularly against known landmarks whenever possible.