Should a professor recommending me talk about my (bad) grades in his or her letter?

It really depends on how the professor knows you.

If the professor only knew you "after the change", the letter might say "I am aware of student's relatively low grades during the first few years, but by the time of my class, they were a top-performing student", that kind of thing.

If the professor has known you for years, it might be appropriate to comment on having observed this change, and expressing confidence that you can handle the role in question despite the low cumulative QPA.

Is it a good idea to talk about your bad grades in a recommendation letter?

If not asked about it, why shed the light on it?

Your professor can talk about your points of strength and your efforts through the years. No real need to talk about everything in details.

If you really feel that the grades by them self are subject to questioning, it will be a good idea to mention them in that way but, in my opinion, everybody knows that the grades alone aren't really a factor and in fact, your grades getting better time after time is the biggest factor.

I would suggest, if you really need to talk about it, to say something among these lines:

X has shown big improvement through his undergraduate studies which proves, with no doubt, that he is capable of handling bigger projects.

I am not a native English speaker so this might need some improvement.

Bottom line is to focus on the good side without really mentioning the bad/down side that got you there.