I have no trouble whatsoever using ye olde google and getting tons of hits that dispute the safety of GM plants in dozens of ways. Plus I have no trouble finding web sites dedicated to the legal issues that have come up regarding GM food.
The moose is waiting. Peer reviewed repudible sources are best. 
GM foods are, by definition, not natural. Fish genes in our tomatoes to keep them from freezing so quickly is not a normal course of events.
Penn Telller made claim that in fact tomatoes with animal genes, while used in the lab are not being sent to the dinner table. Is the claim of the expert they quote correct? I do not know.
Modern medicine is not natural. I am not sure that unnatural implies unhealthy. Sometimes it does.
The ability of a crop to be sprayed with weed killer and not die while the weeds within the crop do die is not a natural course of events. Whenever someone, be it an individual or a corporation, decides to do something major like produce GM products, to calmly accept that all is okay because nobody would ever harm another human for profit is possibly naive.
This is why science based testing, monitored by independent government bodies is required. These bodies need to be at arms lengeth from political control. In Canada, we have this.
Things are going wrong. Hounds Tooth, a noxious weed out west, can currently be treated successfully with Roundup. But the the maker, Monsanto, admits that they have have, through carelessness or some other means, managed to allow Roundup-proof Hounds Tooth out into the wild. And it is slowly spreading out, fanlike, from the research areas on its way to re-infest the land, a newer, stronger variety that won't die easily. Is this something we should not discuss because it is dissing ag businesses, or is it a legitimate concern that is worthy of public discussion?
This sounds like a legitamate concern. Perhaps, Monsano should be sued by the government or chasrged with clean up?
This particular article does not mention the weed I did, or it may be using another common name for it, but I only mentioned one. It mentions twenty types. And notice that Canada is not immune. And the article is from the Minneapolis Post, so this is not a fly-by-night website.
http://www.minnpost.com/earth-journal/2012/05/arms-race-against-weeds-new-weapons-extend-losing-strategyHere is an article that is a couple of years old from the NYT. Same problem, different year.
http://www.nytimes.com/2010/05/04/business/energy-environment/04weed.html?pagewanted=allI have no trouble finding people concerned about Bovine Growth Hormone and the human ingestion of it. People concerned about such things don't seem to be cranks the way the anti-human vaccination crowd is.
See the request for peer reviewed articles on the subject.
My generic store brand milk has a label on it that proudly declares that it is not from cows treated with that substance.
That is good business, the question is, is it good science?
Don't know. Let me google it. Hmmm....
First, we'll ignore that it is also made by Monsanto. I'd hate to jump to conclusions.
You mentioned Canada. Can't get milk with it there. Illegal. Same with Europe. And now in the US only about 17% of the cows are getting it. So apparently it is either a) dangerous or b) perceived as dangerous and not used. Virtually everything I find on Google says it is bad for us, and I can't find much about how refreshing it is, like Pepsi. But if only 17% of the cows are getting it, and I'm not, it is apparently not much of an issue. It should be easy for anyone who doesn't want to consume it to avoid the stuff.
A few articles just to show that I can actually use search engines:
http://www.cancer.org/cancer/cancercauses/othercarcinogens/athome/recombinant-bovine-growth-hormoneA very short and damning story about the product and Canada (damning if you're not big on bribes)
http://wiki.answers.com/Q/Does_milk_in_Canada_contain_Bovine_Growth_HormoneHere is one that thinks the stuff is akin to cupcakes. (Note that my search term was "bovine growth hormone" and nothing else. This first clearly positive story on the stuff was on the fourth page of the search results):
http://www.huffingtonpost.com/jeffrey-smith/court-victory-bovine-grow_b_751009.htmlNow how one group can say there is absolutely not health risk from BGH and another can say it is a proven carcinogen I don't know. But in a case where I can easily avoid the stuff, I will.
I found it interesting that Monsanto was taking people to court to keep them from putting "No Bovine Growth Hormone" labels on milk. Monsanto lost. That's how I know mine doesn't have it.
http://www.huffingtonpost.com/jeffrey-smith/court-victory-bovine-grow_b_751009.htmlIf you eat lettuce grown in California, it has traces of a compound in rocket fuel that, when accidentally or carelessly spilled in that region quickly spread throughout the water table because most everything it touches acts porous to it, and it spreads like wildfire underground.
This claim sounds untrue. How much rocket fuel is there?
I wish it was. And the amount is almost irrelevant. It flows so freely in underground aquifers that even the tinest amount will spread all over hell and gone.
The stuff is called perchlorate, and though it is a natural substance, it is not something that normally contaminates water supplies. And while the health risks of the stuff may be low compared to some things, we don't know that for sure. (The only major health risk I see discussed is regarding its negative effects on the thyroid in women and children. I have seen people link it to cancer, but I'm not finding anything reliable on the subject in my search). It may be measured in parts per billion, but when you drink a glass of water with a couple of quadrillion molocules in it, you get quite a few billion bits of the stuff.
The EPA initially recommended a limit of 1 part per billion in drinking water. The Bush administration said there is no need to regulate it and anything under 15 parts per billion should be just fine. I'm biased, but if the Bush administration liked the stuff, I probably don't.
By the way, once he left office they felt free to regulate, and have regulated the levels in drinking water. So at least the issue isn't being ignored, even if the government is at times sort of incompetent when it comes to stuff like this.
Here are some links:
Wikipedia, for a short version:
http://en.wikipedia.org/wiki/PerchlorateThis is an article out of USA Today, but published in an environmental blog:
http://content.usatoday.com/communities/greenhouse/post/2011/02/epa-rocket-fuel-tap-water/1#.T8V8bpj-tLSThe EPA page on the subject:
http://water.epa.gov/drink/contaminants/unregulated/perchlorate.cfmIf you want a pro-perchlorate page, it has a site of its own! Yea!
http://perchlorateinformationbureau.org/Where they claim that 24 parts per billion are just yummy.
I can't find the article I had read on lettuce and the chemical, but I found others. Like this one:
http://ehp03.niehs.nih.gov/article/info:doi/10.1289/ehp.113-a232aAnd here is the abstract of a study done by Texas Tech in 2003 that found 97% of the human breast milk samples it studies were contaminated with perchlorate. Remember that part where I said it was bad for women and children.
Are we questioning the rocket fuel industry unfairly? Are we supposed to ignore the question because the ag industry is involved and too precious to question?
If these claims are not backed by independent peer reviewed scientific reseach, then yes.
A couple of the above links were to peer reviewed scientific papers.
If we can't ask questions freely, then we can't expect accurate answers. I live in Montana. Much of the state depends on agriculture. I'm in the construction industry, and my job depends on the health of the local economy. he factors causing people to become obese. And I'm sure if I were to read more of my google results, I would find other questionable outcomes to add to this list. Am I not supposed to do that? Read google results?
You are an American. Your country wasfounded on people being able to ask questions, freely.
The hard part is thinking critically about the answers that come back
That is what I'm trying to do. Ask the right questions, get the right answers. It is difficult to parse info accurately when so many points of view are diametrically opposed. I guess I just have to choose sides and hope I'm right.
I don't know how to find the answers.d we have mothers who don't vaccinate their kids because they are convinced shots cause autism.
It all sucks. We are all stupid because we don't have enough information. But please let me ask whenever I'm curious.
Google is a great start. The trick is to ask yourself, how objective the sources are.
Biased sources
The Kato institute
Green Peace
The organization representing the businesses involved.
Most news outlets. I consider the BBC an exception but that's me.
Objective Sources
Harder to find. Some government oganizations. In the US, I'm skepticle that some of their government backed
Research is at arms legth from their goovernment politicians.
I think Canada andthe UK have good reputations.
Peer reviewed papers in scientific journals
REputible Universities
... 
I'm trying. Really I am. This is a good exercise in researching hard questions. And luckily I was breast fed before they invented rockets (well, not really, but the ones we had were powered by pterodactyl farts.

)
Wish us all luck in these matters.
Edit: Fixed pathetic quoting problems