I want to make some house improvements for my grandma. I'm afraid I can overlook some dangers/ discomforts. What are the most important changes that I can make?

Prevent falls and tripping. Remove throw rugs and electric cords on the floor, make sure there is good lighting for night trips to bathroom. Assistance rails beside toilet and in bath tub (anti-slip on bottom of tub or shower.)
If they are frail or have medical issues a Medical alert system for $35 to $70 per month would alert authorities for a medial emergency.

Welcome

What home improvements are you wanting to make, what home improvement experience do you have, and why are you undertaking these improvements.

For instance, if you are inexperienced and trying to make medically suggested home improvements for your grandma because she can’t afford to have them done, there are community resources that should assist you. Like Habitat for Humanities.

We need to know more about what you want to do, and why you want to do it?

Is she frail? Is she getting forgetful? Everything tropical willy said is great. One of the things we did for my wheelchair bound mother in law was to install remote controlled lighting. She physically couldn’t get to the switches and if she forgot to ask her home help to do it, she’d be stuck in the dark at night or the lights would get left on all day. We also made her shower more assessable by removing the door and putting in a curtain. Motion sensor outside lighting made her feel safer at night.
Other things to think about, electric outlets that will automatically turn off incase an appliance like an oven or iron gets left on. Turning down the hot water tank so she is less likely to scald herself. If she has a cell phone make sure you have ICE numbers on it.

Ramps instead of steps can help.
What @cazzie said, plus you can get motion sensor switches for indoor lighting; they are relatively inexpensive and easy to install (you are dealing with electricity however so be careful). Or Illuminated switches. How about clap on/clap off lighting.
Full extension drawer glides in the kitchen and bath and pull out shelving for the lower cabinets so she doesn’t have to bend over or get down on her knees to access her cookware.
Higher than normal countertops to reduce stooping.
Thermostat with large easily viewed readout.
Eliminate sharp corners on furniture where possible.
Shower head on a slide bar so it is easy to adjust the head to the right height. Shower/tub bench.
Remove the tub and replace with walk in/roll in shower or High tech (high price) a walk in tub.
Single handle faucets at sinks and tubs/showers.
Large numbered alarm clock.
Stand Up Assistance Bars or more rigid furniture that makes standing up easier.
Easy Lift Chairs. Lift Assist Cushion
Lever type doorknobs instead of ball type.
Low pile carpeting, non-slip tile, eliminate thresholds where possible
Plenty of lighting throughout, especially hallways, doorways, entries and stairs but also in living and dining rooms. Also, tables or benches at entries to put things down on while looking for keys.

Welcome to Fluther.

To answer your question you need to be able to look at the house as your grandmother would (or could, if her capabilities for discernment aren’t what they used to be), and you need to consider her already-lost and still-failing capabilities.

With older folks, two of the most common are mobility / agility and eyesight.

So be certain that she has “access” everywhere:
– eliminate steps where that is possible (including the “step” into a bathtub, if that’s still present – consider replacing with a shower stall – including a seat – or one of the newer no-step tubs);
– watch for tripping and sliding hazards, as others have suggested;
– be certain that hallways and all walkways inside and out are free of obstruction and have some way to either catch a fall (handrails and handholds wherever they can be provided), or a way to help her get herself up when she does go to the floor for some reason (sometimes by choice, for example, to retrieve something on the floor);
– put all common utilities on one floor.

As to eyesight, make sure that she has adequate lighting everywhere she will need to be. If necessary, provide extra lighting in closets and otherwise normally-dark areas.

Check frequently for burned-out lamps and replace as needed. You won’t want her attempting to change light bulbs overhead, for example.

Check smoke detectors twice a year, as recommended by manufacturers and fire safety professionals.

Make sure that her water heater is not set to a potentially scalding level.

Provide magnifiers to see settings such as stovetop / oven dials and indicators, thermostat and thermometer settings.

If she uses a landline phone, get her one of the newer ones with oversized and lighted buttons for both vision and access. Pre-program commonly called numbers, including your own.

Get her a “grip extender” so that she can reach things from overhead closets and things on the floor without having to bend or get down to get them.

There are also all kinds of kitchen products for people whose grip is not what it has been, such as vegetable peelers, can openers and tableware with oversize grips.

You might also look into “lever” door handles instead of the traditional “knob” handles that have to be gripped to rotate.

Consider shelf units for clothing instead of dressers with drawers and pull handles.

I nearly forgot one of the most crucial elements to independent elder living: Some kind of Life-Alert device that she can wear 24/7 to call a responsible and local service for immediate emergency service from any place in the home, whether she is near a phone or not.