You identify three issues:

*blotchy staining, which likely means inadequate coverage;

*cracked concrete, which indicates lack of proper control joints;

*scratches put in the floor by the electrician, which is the electrician's fault.

If there's no sealer on yet, the first and last problems may be rectified.

But it looks like the company you chose was in over its head.

I am looking into stained concrete floors in my home as well. I have spent a lot of time looking into them. To answer your question I would say that although it is not what you wanted it is typical. Through my research I have found several companies that used to do the staining, but no longer do because there are soooo many ways for it to be ruined. Even painters tape can ruin a stained concrete floor. It sounds like the problems started early on like maybe the concrete was not prepped correctly. It has to be cleaned a specific way first. I think that may be why some areas didnt stain right. I cant speak for the cracks. Unfortunately, the electrician probably didnt know any better. I have seen pictures of a kitchen that was COMPLETELY ruined when installing the appliances.
Do you have any recourse with the builder or the person who stained the floor?
I am so sorry to hear this happened to you. Stained concrete floors can be very beautiful. I am thinking that I am going to do whatever it takes for my concrete floor to be the absolute last thing that is done in my new home.

It sounds like you have more issues with the concrete slab finish than the staining job. Its usually entirely different subcontractors. If its not sealed yet, you could stain again. Different but similar colors can make very interesting results. Sounds like its too late for a polish job.

If your question is "is it normal for stain to be blotchy?" Yes. As for a completely uncolored area, No.

Ive had better luck with sealer sticking to rough concrete than smooth. There are colored epoxies meant for control joints that might be worth a try for your cracks.

Personally, I would probably prefer a rough, cracked stained concrete floor to wood. But I really like stained concrete.

The concrete was poured during a really hot/dry time and we were not able to keep it hydrated, which I think helped promote some cracks. Also, we didn't have expansion joints. The guy that poured the foundation is also the one that stained it. Hindsite, think that was a mistake. He is a great worker but not an expert with staining concrete (obviously). We should have just gone with wood in the first place! Oh well.
Sprintime-the small cracks are fine and actually do give a more interesting look, but the large cracks, well... And the spots that did not pick up any stain...

I guess we didn't do our homework on stained concrete either. Lesson learned.

Thanks guys.