Probably 2 of the most important areas I focus on when teaching is improving technique and enabling the player to turn theory into music.
Improving Technique
The only real way you can be sure of A) That you need to improve B) whether you are improving - is to hear yourself playing. It is an interesting fact that when you are playing the guitar, it is very difficult to actually listen to what you are playing. Hearing yourself for the first time "on tape" can be quite a shocking experience. Likewise, once you have practiced and perfected your piece it can be one of the best feelings in the World!
A proper recoding device will enable you to record, listen to what you have played and at this point you can "disect" your playing and begin to appreciate where your weaknesses lie.
A 4 track recorder is one of the best investments any guitarist will ever make.
Turning Theory Into Music
Once you have had a few lessons, you will be taught that certain chords fit nicely with certain scales. Unfortunately, so many players are put off the "theory" so unnecessarily simply because they do not put the theory into practice.
An example..
In the key of C, you could play the following chords C Major, D minor, E minor, F Major, G Major, A Minor and they would all sound nice whilst heard over the C major scale.
Now this might sound dull, dull, dull on paper - but try actually playing it! It will open up a new World of music!
Get the 4 track recorder out. On the first track you could play the chords - say 4 strums of each. Simply rewind the tape and set the second track in action and this time you are hearing what you played before but recording the scale over the top.
What you now hear is how your scale tones seem to weave in and out of the chord tones, some working better than others. What you are now doing is producing music! Inspiration at last!