Scott, it looks like you may have had a slab where they took the forms off too soon and the edges cracked away, so they fixed it by laying some portland or maybe sand mix over the crack and troweling it smooth. Either that or the mix was bad, too wet, or too old at those two points.
There is no real way to fix it, other than replacing it, or capping the whole thing. There are some overlays that you could put on that may work, but overlays depend on the concrete underneath being sound. There are also some "concrete repair" mortars that you could try, but I have not had good luck with them, especially in appearance.
Looking at your feet (g), it appears to me that this is calcium deposits from hard water. The landscape rocks seems too suggest you are in an arid climate. Is there an irrigation system near the cement?
Nothing to be alarmed about. Try a vinegar spray, allow to set and repeat the process (pour it on full strenght, sit for awhile and rinse).
We get this on block walls and pads. I think it's called Efflorescence (?) You won't get it cleaned up, untill the water/ moisture is stopped.
You don't mention the size of the porch area but I would suggest a non-skid floor tile and a bull nose tile set to the edge in a color that would flatter the entrance way. Get a tile setter for a quote and an opinion before breaking out a sledge hammer. Construction work is slow. This is a great time to find someone to take on a small job such as this.
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