A good example to show you the issue is:

"There has been a change of schedule." = We now have a new schedule, instead of the old one.

"There has been a change to the schedule." = We have the same schedule, except for a particular change.

So if the course of a river has to be corrected, then we can either consider it as producing a new course ("correction of the course of the river") or making a particular change to the current course ("correction to...").

There will be some situations where the same change can be considered in both ways. 

correct = original meaning to set straight.

correction of = the correction made by somebody or a machine sensor etc. 

correction of = the amount of correction applied to set straight, to correct,

correction to = what the correction was applied to 

"a correction of five degrees is needed to avoid a collision" 

"a correction to the steering of five degrees will avoid a collision" 

"the teacher made a correction to the students essay"

"the student appreciated the teachers correction of his essay"  <-- students essay is being possessed by of/his

There are cases when there is overlap in meaning and of and to can be interchanged.

"the corrections of Professor Val to the theory, resulted in resolving a long term problem" 

"can somebody please help me and make corrections to my writing"

corrections of = the corrections made by somebody the "of" = possessive. From of the person making corrections. 

Corrections to = the corrections made to something. 

This is the simplest way I can think to explain it without delving deeply into the linguistics and grammar. 

I am sure others will soon appear to explain the grammar points, for you.

John & Michael,

Thanks a lot for your help,

now at least I have some idea about this difficult for me subject.