Plastic Chef Neelix
"What kind of cook thinks that increased heat equals less cooking time? A bad one!" -- Chuck Sonnenburg.
Neelix does not respect the tastes of others
It is something that that many good chefs are known for is to tinker with recipes in order to improve upon them or to overcome a missing ingredient that isn't available. Neelix does not do this well and in fact he finds ways to force his own versions of dishes on those he is serving even when every part of the original recipe is available.  He seems to think that no matter what he is told that his special additions are always an improvement and is flummoxed at the very idea that someone could dislike his new version of the dish. This includes the additions of spices that he is constantly told that the patrons can't stand.
This goes so far as to insist that when food is smuggled out of his kitchen because someone wanted to make a dish their way rather then his, some type of punishment is required. It's understandable on a minor level that he would try to convince people that using locally available supplies is a worthwhile effort, but if something does not please the pallet of a patron, you shouldn't force it onto them. No, this is not the same as convincing children to eat their vegetables, as the items he insists on adding are only flavor enhancers, not items of any real nutritional value. The impression is that if someone was allergic to something, he'd still put it in their food and make them eat it anyway.
Neelix always cooks his food on high
It's somewhat understandable in the context of filming something cooking on screen to use an obviously visible flame, but what we see Neelix doing goes well beyond that. In every cooking operation we see Neelix doing, he is always doing so with the flames so high that fire licks up to sometimes half the height of the sides of the stock pot he is using. This helps explain why we see Neelix overcooking or even outright burning food on multiple occasions. Any good cook will tell you that those kinds of heat levels are only useful in a vary narrow number of applications: wok based cooking is a good example.
Ignoring that, such high flame represents a massive waste of resources. We are constantly being told that power reserves are precious, but we then see Neelix overusing energy to cook the food that is suppose to be helping. No matter how the technobabble is explained to us, it doesn't change one the fact that energy is being used very inefficiently to do tasks where not even close to those levels are required.
Neelix thinks that higher temperatures equals faster cooking times.
This section is partially related to the previous point, but it showcases a different cooking-related issue. In the episode "Flashback", a technobable material in a nebula is discovered that Neelix says they could inject into his cooking array, allowing him to cook meals in half the time. Because of the level of techno gibberish in this scene, it's isn't immediately obvious what assumption Neelix is making.
To make it clear, doubling the combustion rate of his burner is suppose to half the time his cooking will take to finish. This leads into something that is often called "Oven Logic", which is a mistake made by many amateur cooks. Doubling the power of your burner does not half the cooking time (or any other linear expectation) because of the complex chemical interactions that take place whenever you cook anything.
Neelix lacks even basic sauce making skills.
Neelix is seen in the episode, Learning Curve, to be making macaroni and cheese where his solution for making a cheese-based sauce was to take a chunk of solid cheese and just toss it into a pot filled with macaroni and leave it at that. While with some soft young cheeses (and certain blue boxed mixes but that's butter and cheating) this is possible, even with those kind of cheeses an experience cook will melt the cheese into a separate saucepan and integrate it into a sauce then add that to the pasta. Also this is another place where his inability to ever turn down his burners will generally spell disaster as the pasta would be very over cooked before the cheese will become anything close to a stable sauce.
His high burners also means that when he is making a large amount of a spaghetti-type sauce he is required to make use of constant tending of the stew-pot that the sauce is cooking in in order to prevent it from burning. This is something that does not tend to produce a tomato sauce that will have much of anything that could be called good flavor or texture. This may be the reason Tom Paris expressed annoyance at the quality of his Spaghetti. 
Neelix does not seem to understand basic food safety principles
Once again we are forced to look to the disaster that was Learning Curve. Neelix has made a batch of homemade cheese and the manner he is storing this cheese is in a bell jar-like container on the counter in his kitchen. While there are a few cheeses that can be stored in a room temperature state(none of which Neelix had the resources to make) without much worry most experienced cooks will still store them in a refrigerated environment as that is just one extra precaution against food poisoning. The danger-zone is a very real concern and as evidenced by Neelix managing to infect the ship itself with his cheese just begs the bigger question of how many food poisoning cases was the Doctor dealing with that they just didn't care to show us.
Neelix solution for cleaning greens for use in a salad was to shake them off and set them on the counter. 
Neelix is not a good example for anyone on how to operate a kitchen in any sense of the word. It is a sad reality that a cook book has been produced featuring Neelix on the cover. I'd rather see the book with Sisko on the cover as at least he seems to know what he is doing. The sad part of this book is the recipes that had to have been created by competent chefs that are now associated with this insult to culinary arts that is Neelix.