After all the new regulations travelling to the US if you have dual nationality with Iran or did visit it in the last 5 years as a tourist or for buisness, I doubt that Iran will lighten up on US citizen.
@michand1 What did you write on your entry/customs card in the US for "countries visited on this trip"? Did you admit you had gone to Iran? Since your visa would be in your non-US passport...did the airport officials not care that you had been to Iran but had no stamps?
Also, when you were checking into your flight at LAX (or wherever you departed from), did you show your French passport at the airline counter? It seems you would have to, since the visa is in there and I assume they wouldn't let someone with an American accent check in for flight to Iran without showing proof of visa. So does this mean you also entered your French passport number when originally purchasing your flight?

Responding to above.
NAUGUSTYLE: No one asked me if I was on a tour. But I was careful to not immediately identify myself as American. Not out of concern for myself, but to not accidentally put in jeopardy some innocent person on the street curious to know where I was from. To then have them questioned how they knew an obviously unaccompanied American. I was careful for them just in case. But I never sensed there was a problem. When people asked me what I was, I initially kept it vague. I said (truthfully) my Dad was American and my mother French and I live in California. But never because I felt there would be hostility for revealing I was American. They liked I was French, maybe even more so I was American. I just eased into it. The only time it was an issue is when I shared a driver/guide with a German woman The man told me he could drive her but not me since he didn't have the authorization for Americans.
He relieved after he saw my French passport and Iranian visa.
SINASINA: Correct. You do not need to arrive via Tehran. I arrived via Isfahan.
LUCAPAL: I find the story fishy unless the person was hosted by a local. Even if an American did manage to slip into the country as part of a fake tour, I think you'd be a fool to try. You're breaking the law. You'd at least be deported and never be allowed to return. Maybe made an example of and shown the hospitality of the prison system. For one thing, when you check into a hotel they take and keep your passport. They can't legally rent you a room if you're an American traveling alone. Do you sleep in the park?
NAUGUSTYLE: Returning to the US I used my Global Entry Pass and US passport. With Global Entry there isn't a paper form like the one you get in the airplane. I correctly entered the countries I'd visited in the machine, got a receipt, and handed it on the way out. The agent may not have even looked. As a "trusted traveler" there is less scrutiny, but I had nothing to hide. An acquaintance of mine who is also a US/French citizen, and who has to fill out the normal paperwork, has returned from Iran several times and has never had a problem. Remember: Americans are not prohibited from visiting Iran. The current problem--due to recent terrorist attacks in Paris and San Bernadino, California--is for dual-citizens of visa-waiver countries like France, Germany, Australia, whatever, who are also (let's be realistic) citizens of an Arab country and have been to Iran in the last five years. That's a "red flag". There is legislation in the works where they could have trouble getting into the US in the first place. Unless they first got visa in their home country.
Regarding being able to board a flight to Iran, the airline is very careful you can legally enter Iran. But that is for the flight that flies there. I spent three days in France and three in Germany before entering Iran. Prior to boarding my Turkish Airways flight from Hamburg, I had to show my Iranian visa to the airline. But having a visa prior to boarding is not necessary if you have a passport from a country where Iranians allow a VOA.
I don't think it matters what you put in your airline reservation if you have two passports, as long as you can legally go to the country that is your destination. What's important is the passport you show when you get your boarding pass. And if questioned, so what you have two passports. So what? It's common.

Just apply with the Mexican passport. There is a question if you have another nationality. It does not matter. It is obvious from your application where you live etc. They will not issue your visa number and give you the visa if they had doubts about you. It all gets vetted at the Ministry of Foreign Affairs. That said, are you going on a tour or independent? If you are independent then you have to use your Mexican passport as that is not possible with the US passport - only organized tour.
Following this thread now... I'm considering visiting Iran in the next few weeks and have a Canadian and Mexican Passport. I live and work in Mexico, so that should be good (and got my passport there), but I was born in Canada, and am currently in Europe. I got into the Schengen zone with my C. passport and assume I need to leave with it.. so I'm partially worried about carrying both into Iran.
Especially after reading this thread, I'm starting to lean towards VOA instead of applying ahead of time due to the possibility of fishy sites, the time involved in the processing times, and then having to actually go get the visa... Seems like VOA ends up being much easier/cheaper than doing everything beforehand.
Another issue I have is that I have visited Israel... no stamp on my Canadian passport, but I do have Egyptian border-crossing stamps, though I assume this shouldn't an issue since 1.) won't be using this passport and 2.) I read somewhere that as long as you went more than a year before going to Iran, then you should be fine. I went in 2012.

I read somewhere that as long as you went more than a year before going to Iran, then you should be fine. I went in 2012.
Irrelevant. Any evidence of a visit to Israel will mean you cannot enter Iran.
Use your passport from Mexico to enter Iran, and use it whenever you are asked for ID as this will contain your visa and entry stamp. Don't worry about carrying your passport for Canada, but don't show it to anyone, either.
You know about the need to carry all your spending money with you, I take it.
I'm starting to lean towards VOA instead of applying ahead of time due to the possibility of fishy sites, the time involved in the processing times, and then having to actually go get the visa...
It's not really that complicated. The only time-consuming part is applying for the visa at the consulate that you nominate, and it may take a couple of days for processing or you may get it instantly.
However, the Persian new year (Nowruz) is coming up in in about 10 days and this will delay processing for visas as everyone winds down for the big holiday. It also means that accommodation and transport will be much harder to get during the 14 to 21 days of the holiday period.
Re: $, yep.
Re: Persian NY: Sounds like even more reason to go for the VOA.. I was planning on going to Iran in the second week of April, give or take a few days.
Having grabbed my Mx passport just now, I'm worried about the fact that it has absolutely no stamps....
Haha, I know the feeling. I guess whenever I do this, my other passport will be pretty new so...it will be easy to understand that it's stamp-free?

It is true it can be assumed someone went to Israel by Egyptian border-crossing stamps, yes. But if you are going on a clean Mexican passport there should be no worry. The rules don't say you can't travel on a new passport. The rules do say your passport cannot contain an Israeli stamp. So having also a Canadian passport with suspicious Egyptian stamps suggesting travel to Israel would only be a problem--I assume--if your were thoroughly strip-searched for some reason, and it was discovered. And even then would it matter unless they were looking for a reason to deport you?
When I used my French passport to enter Iran no one asked if I had another passport. (I did: as US one.) I didn't live in fear and paranoia. I tried to appear someone of "good character" respectful of local customs. Not someone who would endanger their morals. Just common sense. I didn't dream of looking for alcohol or touching (the attractive) local women.