The difficulty of sharpening keeps a lot of people from using serrated knives. There are tools and methods that make it easier, but it is always more work.

There is also a belief that serrated edges are unnecessary because anything they do can be done with a plain edge. I view that as similar to saying that any wood can be cut with a carpenter's saw so chain saws are unnecessary. Serrated edges are much better than plain edges at cutting any kind of fibrous material (like cloth and rope).

I am also not convinced that serrated edges do any worse with most other materials. In most cases they are less precise, but faster. I wouldn't want to whittle with one; almost everything else is fair game.

Combo edges are often picked on for not having enough of either to be useful. If you are making cuts longer than an inch or two most combo edges will "run out" of whichever edge you're trying to use and require you to make another stroke. There is some truth to that. I prefer fully serrated or fully plain edges for that reason, but I almost always carry one of each. Combo edges are a compromise, but I don't think they're a bad one. It depends on the types and sizes of cutting tasks you do.

One real issue with serrations is that many of them just are not very good. I think the widely held belief that a properly sharpened plain edge will cut better than serrations is based on how badly many of them work. There are also some very effective serrations. The best known, Spyderco's Spyderedge serration pattern will easily outcut a plain edge on many kinds of material.

This is one of those topics where a lot of people have strong opinions. Like most such topics, some of those opinions are solidly based on personal experience and a lot of them are based on hearsay and prejudice. I would like to think mine fall into the better category, but then, everyone does. :-) Take all of them, including mine, with a grain of salt.