
It looks to me like it's just a support piece nailed into the wall with a 2x4 running across as a step. They go down to our unfinished basement and a few of them are starting to fail.
Anything I should be aware of?

It looks to me like it's just a support piece nailed into the wall with a 2x4 running across as a step. They go down to our unfinished basement and a few of them are starting to fail.
Anything I should be aware of?
If the cleats supporting the steps are solid and haven't deteriorated, use 3 inch course-thread screws to re-secure them to the stair stringers (the long outer sections that span from the bottom to the landing.
If you are in doubt as to the condition of the cleats replace them. I'd use any 2 x stock cut a bit longer than the width of the step. Install it so the cleat's edge is recessed back from the step's edge. From the looks of your foggy photo it appears your steps are 2 x ? stock. If they are in need of replacement (and can't be repaired) replace with similar dimensioned wood.
Also you might want to consider if there are several steps and/or cleats to be replaced is to install a third stringer between the existing ones. They can be found sometimes pre cut. And it isn't that hard to cut one from a length of 2 x 10 or 12 Douglas fir.
Yes, what you should be aware of is that the guy who built these stairs is a moron. You cannot build stairs like this.
Get a book like Building Stairs (by Pros for Pros) so you know what you are doing.
-------------------------------- Response to the Comments
First to the OP: if you want to fix your stairs right, get a book like I have linked and do what it says.
To the would-be stair builders below who seem to think cleated stairs are a good idea:
Stairs are like furniture; they have to hold together. Trying to use $100 in bolts is not going to save you. Wood bends and twists, especially the soft wood used in OP's construction. You could add 10 pounds of bolts to that thing and it will still look like a Bonsai tree in 10 years. Trying to secure a 30 inch tread to a half inch wooden cleat is just not a good idea that will not work in ANY scenario no matter how many bolts and screws you use. Sooner or later somebody is going to be carring a 19" TV down there, the tread will bend and collapse and they will fall.
Unfortunately, I can't do a Vulcan mind meld and make you understand why softwood stringers with softwood treads and softwood cleats will pull apart over time. I suggest reading a book on cabinetry. To hold wood together you have to bind it in every direction properly. Pounding in a few nails or screws to even a 1" hardwood cleat is not going to do that. A 1/2" pine cleat is a joke. Softwood stringers with only a one-dimensional fastening (no risers) will always bow and twist. Even if you use expensive, heavy duty steel angles, (obviously not the case here) they will still twist and fail eventually.
Can you engineer stairs with cleats? Yes, with enough steel and a proper two-dimensional design , it is possible to create permanent stairs using cleats. THE OP IS NOT A STRUCTURAL ENGINEER, SO HE IS NOT GOING TO DO THAT. The proper thing to do is TO READ THE BOOK I LINKED and do what it says.