I would definitely ask the director to specify when your son has been using inappropriate language, as his teachers have not mentioned it. Also get the details on what led up to the incident witht he other boy. Was it a sort of competition, like you mentioned, or was he angry and wanted to hurt the boys feelings? Heck, I've even seen kids this age say things like that in play and they were both fine with it (because they were pretending) until another child jumped in and said "he just told you x y and z, aren't you mad at him now?".
As for where they get it, who knows? Heck, just last week my dh overheard my son use the f-word in the correct context. I thought, wow, after 8 years of hearing this he's finally figured out it's a cuss word (assuming that he'd heard it from me, of course ). Then tonight in the car he told me that one of my daycare kids taught it to him when they were playing football. Guess I'm off the hook for that one.
Definitely need to investigate this further. Your son said things that need to be addressed. Firmly and thoroughly, no matter how difficult it is for you. If he said it, he is mature enough to discuss it. The teachers need to explain why they haven't said anything before.
For the sake of your son, do not take either side of this lightly.
I would get the exact words from the director and then ask your son where he heard them. I would want to get to the source. And don't worry, this really isn't that big of a deal.
I say your child may have heard the violence and swear words by other kids or others around them but parents always get the blame. Even some cartoons are violent could be anywhere. As far as the "my daddy is better than yours" type of deal all kids do that. This is a tough one but yes definely talk to this director and ask how long is this thing going on for one day it is great then the next problems for it does not make sense.I was never a daycare director, but I WAS in charge of the 3 year old room, and at the end of the day all of the children were combined, so I heard plenty of this kind of talk...maybe I am too laid back, but I am not even sure that I would have done much more than explain to the children myself how that kind of talk was inappropriate....
But, since this teacher and director have gotten so involved, I think that you are on the right track. Tell the director (in writing, since she did so) that while you fully understand that the incident(s) needed to be addressed, you find the tone of the letter offensive, given that this is the first you have heard from any of the teachers of either child, and you inquire daily on their behavior.
Then talk with your children about proper language...I know a lot of the children that I have taught over the years (3-5 years old) have had "salty" language. All we ever did is to tell them, "We do not use those words at preschool" and leave it at that. I think that the more the teacher gets upset, the more weight the children are going to place on it and the more they will get upset...
We also would tell them that when they began to talk about having boyfriends and girlfriends...."Preschool is too young to have a boyfriend/girlfriend, we can all be good friends."
Does he have to be put in the same environment as the younger children...perhaps they can bump him up so he is with the older kids ?Boy, things were going so well for M at school and daycare, and all of a sudden some issues again 
First of all, one of the teachers talked to me last week, saying that M (5 yo ADHD, on meds) had come up to one of the preschool children (they combine classes at the end of the day so he was with the younger kids) and said that his daddy was going to kill their daddy. The child was upset, the parents were upset, etc. We talked with him about it, and told him that he absolutely could not say words like that ever, that he really scared this child, etc. and that if we heard of him saying anything like that again that he would be punished, and kind of left it at that.
Well, yesterday, I got a letter home from the daycare administrator. Now...I totally understand that they felt that they needed to address this with us, but the whole tone of her letter really offended me, and I am not sure how to handle it. She started the letter saying that she is concerned about "the words that come out of M's mouth" - which to me sounds like she is implying that he is using swear words and inappropriate language on a daily basis, which I don't think he is. If he is - then they have a problem with their teachers because they have not said anything to us for quite some time, other than this one incident. In fact, most of his daily reports home have indicated wonderful/good/excellent days, up until the last couple days anyway. But now she is saying that several parents have called, from M's class and also the preschool class about him saying that - but she declined to let us know whether he had multiple incidents of saying it or if he said it once and several children heard it. She also did not say whether it was sort of a provoked comment - like a discussion of "my dad is better than your dad" "My dad is stronger than your dad" and M came out with that comment that is extremely inappropriate but maybe he just didn't think about what it really meant when he said it, or if he just unprovoked walked over to a child and said it. Not that why he said it makes it any better or worse, but it would help us in talking to him about it, and also talking to his doctor about it.
Then she also said that they have "heard swear words come out of (your 3 year olds) mouth". Again, I was offended by her choice of wording...plus, I have to honestly say that I can only remember 1-2 times in the last year when our 3yo has said a swear word...and I know that he didn't really know what he said, so we ignored it and he did not repeat. His teachers have also never once said anything about this to us, but now she is putting it in writing.
Then she goes on to talk about how some parents think that "kids just say things" but that with parents calling she needed to address it with us. She should know that we are VERY proactive where M is concerned - we are very much in contact with both his 4k teacher as well as the daycare teachers - if he has a bad day one day, I often will call the next day to discuss and see how he is doing. We have never tried to shrug off anything that he has said or done and ignore it.
So, my questions are: how do I address this with M, and what do I say to the letter writer?
With M, I think that I will have a conversation with him about the difference between getting "killed" in a video game, or "shooting" in a video game and in real life. And how he must never ever use those words with his school friends, in any context. I will then let him know that if we hear again that he has done it, we will punish him by doing (x) for 1 day, if it happens again it will be 2 days, then 3 etc. The only things that really would affect him would be no gameboy or no tv.
I think that I will let the administrator know that I found the tone of her letter to be offensive, but acknowledge that I understand why she had to write it. I also will ask her to find out from the teachers what if anything, they heard or observed.
I don't know where he got this! He does not watch violent cartoons, any video games he has are rated for young children (PacMan, Herbie, Monsters Inc) and if dh or I are watching action shows/movies, we only do it after kids are in bed or if they are in another part of the house doing something else.
Sorry so long!!