Throw in several more of the triangular bandages. They don't take up much weight or space and I know I need a lot of them for splinting or slings. They can be cut from old sheets if you can't find them easily.

Add a watch even if you are usually wearing one.
It does not even need a band, really, just store it with the notepad and pen. It could even be stuck to the note book. A sweep second hand is preferred. Timex is more than good enough.
You will use it for taking pulse and counting breathing.
It is good to note down the time when you do stuff too.

If the kit is in the car you could put an old blanket or two with the kit. Wool blankets are great, synthetics are OK.
Injured people get cold fast, especially when on the ground. Whatever helps keep them warm.

Add a CPR mask. It will give you piece of mind when doing CPR or any other rescue breathing.

People have different opinions about what they want to have with them. I would likely never bother to use the tension (elastic) bandages in a first aid kit.

I do tend to use up a lot of cloth for padding though, so +1 on extra gauze and 4x4pads. I would likely add a couple more abdominal pads too.

A bottle of sterile water or standard saline solution comes in handy for flushing dirt, oil or other chemicals out of wounds if they are contaminated.

If the water bottles have an eye cup with them there is your eye washer. You can even get eyecups that screw onto the bottle.

Add some sugar, sugar syrup, or other sweets. This is for diabetic emergencies.

Add any special items for any medical conditions you or people you are near might have. (heart pills, EpiPens, etc)

If you happen upon somebody with a sucking chest wound you will want something to make a flap valve for them.
If your bandages are in plastic baggies you have good material for that. If not you might want to add a plastic baggy or two.
Baggies are good for putting anything personal the injured need to have with them when they are transported too.

Take the first aid courses. The life you save might be your own.