My two primary (I have more) objections to GMO are:
1) Lack of rigorous testing, especially long term testing. Many of the GMO products in production spent a minimal amount of time in the lab before being selected for production, with little to no long term testing being done. (to find any number of potential issues and side chain-effect issues that can happen.) For example, while at the sequencing company, I learned that it's not just about the genome of the thing itself, but it's surrounding microbiome, which of course is almost an after thought to the big-ag gmo producers.
2) The way in which the pro GMO big ag has essentially corrupted the bodies set up to regulate itself. Monsanto is a perfect example of this, but only one of many. They have a supreme court justice who has refused to recuse himself on cases with obvious conflicts of interest. They have a massive online pr (read: propaganda) operation to keep these things out of the limelight or at least remove them quickly. They have basically taken over the most prominent FDA positions. They abuse K-street beyond what even most of the K-Street abusers do. It's this kind of systematic corporate corruption that makes me sympathetic with those who are anti-gmo.
I also have a huge issue with the whole patent system when it comes to genomes, the system is broke enough for normal tech, but there have been some dangerous precedents set that I don't have the time to get into but they will have major consequences as sequencing costs and manipulation costs are reduced and therefore it becomes a more prevalent tech.
Now, all that being said, I see a ton of FUD on the anti-gmo side that is easily refuted, but the problem is that I far too often see the illogical/irrational FUD of anti-GMO being the strawman used by pro-gmo people against the more reasonable and scientific anti-gmo arguments, which seems to be intellectually dishonest, very much like I find articles like this.
I could go on, but just wanted to offer a quick two-cents.
Oh, and don't even get me started on the horrible state of peer-reviewed science. As a layman with a huge interest in science, I held the process up on a pedestal, that is until I saw it from the inside. Bad science abounds and is rarely challenged, which only gives fuel to the anti-intellectual/anti-science movements which is the last thing we need as a species!