Discussing time limits in the limitations section? Is it common to discuss the fact that one didn't have time to do more reading, or didn't have time to elaborate certain sections, in the "limitations" section of a thesis?
No. It not common, nor should you do it! As paul garrett pointed out, this type of excuse makes it seem as though you didn't care or couldn't be bothered to do a better job. 

I would add also that no matter how much time and effort you have put into developing an idea and writing your paper, it is almost inevitable that there will  be something that you missed or could have done better had you had/taken more time. Even the magnum opus on which you have spent your entire lifetime will be superseded by better or more complete thoughts; this is an inevitable reality of academic writing, and not one you should apologize for. 

Perhaps especially as a student, one struggles to find the balance that represents maximum output for minimum time spent. Knowing when to 'let go' is a function of maturity and experience. When you've made that decision (or have had it made for you, due to time constraints outside your control), accept that this might be better, but don't apologize for the inevitable.