Yes first aid kit stuff expires and yes it should be checked/replaced on a fairly regular basis, especially the stuff you keep in your car because it is subjected to temperature changes. Those chemical cold packs that have the bubble of goo you pop into the surrounding sandy stuff can crystallize and become hard as rock over time, making it almost impossible to mix when you finally need it. So even though you haven't used it, it still might need to be replaced.
I'm required to keep a kit in my car by law for work. In addition to the basic stuff you get in the pre-packaged kit, I've got an eye wash, a blanket, flares, reflective traffic cones, visi-vest, flashlight with batteries, small stash of snacks and water, tool kit, string, matches, and one very scary looking utility knife capable of chopping branches off a small tree. Depending on the day, I also have a full-size fire extinguisher, but I don't like keeping that in my car when I don't have to. I don't work in the wilderness, but I do get out in the proverbial middle of nowhere and I have to be prepared to slide off the road in Canadian winter and not die overnight. My car has become the family joke as people randomly name survival and safety gear to see if I have it in my car. More than fair chance I do.
So far, the most useful stuff I've used the most of is that stretchy bandage that sticks to itself only. I've fixed up a few scraped doggie paws in addition to my own. I'm allergic to the adhesives on regular Band-Aids, and not just a little redness allergic... I'm talking full out, it gets ugly. I love 3M for inventing that stretchy stuff.