It's a bit hard to tell until the grout is cleaned up, but it looks like there is unacceptable variance in the spacing and excessive lippage. At the very least, the sloppy grout cleanup shows little pride in workmanship.

"he contractor says it is fine but they could clean it up a little if I want them to"

Oh, MY, my, my ....

That is just horrendous! On so many levels - where to start: First I am no tile expert, but with a little help from a tile guru here (Bill Vincent) I installed subway tile over my laundry sink.
It is hard to tell from close ups - but it appears the tile was not even laid out properly - the botch job in the corner tells me that. It appears there are variations in the depth of some tile as well as some appearing to be off center - that is elementary especially since you are installing a relatively straight forward easy product. Ceramic subways - If you were dealing with stone, or a hand made tile, the difficulty level goes up as does the variation.
- The grout is the easiest part of tiling and this installer managed to make it appear that it was 2yr olds playing with plaster of paris - Please tell me why it is ALL OVER the underside of your cabs!!!!!!! UGGGHHHH I would have a hard time not causing physical injury to someone that did this to my cabs. The longer that sits on the more difficult it will be to get off. Not to mention that on the tile itself he didn't see fit to properly wipe that down
- Last & certainly not least this bafoon put grout where counter meets back splash. Again, elementary - where you have change in planes you use siliconized chaulking - or variation thereof (tile experts can weigh in on that product)

- This just burns me up - it appears the whole thing needs to come down - At this point the installer owes YOU money due to the damage done. Please tell me you have not paid in full. Did the counter fabricator & tile setter come from same place.

- Put hold on check, refuse to pay - and get someone who knows what they are doing to fix this

So sorry
-

Here is a link that might be useful: The rest of the mess

...the contractor says it is fine but they could clean it up a little if I want them to. He said the variation in thickness and texture is normal construction and I can't expect it to be perfect.

If you want? Normal construction? Fix it up a little? Does he think you were born yesterday? That grout is incredibly sloppy, like maybe the guy had never actually grouted before, didn't have a teacher, and neglected to at least read a description of how to do it.

Just for starters:
-There shouldn't be any grout haze anywhere on the woodwork or painted walls.
-There should be no grout "outside the lines."
-That mess where the tile meets the underside of the cab is inexcusable.
-Did he use the wrong product on the line of tile next to the granite? I think he did.

This isn't "just fine." It's an unprofessional mess. Fortunately, it looks like it can be fixed, but be sure it's their elbow grease doing the fixing, not yours. Sorry to say, but you're going to have to call the contractor on his..bologna.

I, showed your pictures it to my husband, who is a GC, he said that cannot be a real contractor, who did that kind of work. And then tell you, it look's fine. Tell him, this work is clearly not going to pass. And they should come back and take some pride and clean their mess up.

Oh my goodness. That looks horrible. I'm so sorry you're having to deal with this unskilled, unethical guy.

Poor you! And you picked one of the simplest tiles... no weird thickness problems, clean edges, uniform size. Your tiler definitely needs to fix it, although I wouldn't have much faith in the workmanship after that. I might think of getting him to take it down, then refunding your money so you can hire someone else or DIY.

Jejvtr is right... the grout meeting the countertop is a real no-no and will give you lots of trouble with house or seasonal expansion/movement.

Your profile says you just registered today... perhaps start by searching subway tile pictures (the search bar at the bottom) or the same search at houzz.com (or even google images) for comparators. IMO there's nothing acceptable about the work as it is.

Hopefully you have not paid the hack everything.

It is an absolute C##P job.

I hope you have money held back, because you're going to need it. You can't just "clean it up", because you need to chalk line the work to level, and then install the tile. He was totally unprofessional in his dealings with you. Tell him that you are rejecting this work and it needs to be redone. I would with hold the cost to redo the backsplash and not allow his tile person to fix it. If they can't get it right the first time, they won't get it right the second.

Hire a new tile contractor.

I think it's all been said...I have a ten year-old that could do better work...

(Laz shakes his head ruefully...)

I take back my opinion on whether or not this can be fixed vs. taking it out and starting over. I defer to those who are much more knowledgeable than I am - you should listen to them, demo this, and start over with someone who knows what they're doing.

10 year old?? I think my barely six year old could do better. I've tiled before and learned as I went. Even my first job was a thousand times better than that. I'm so sorry you're going through this. I, too, would worry about the damage to the surrounding material.

Please don't accept this mess! Looking forward to a positive resolution for you....

Thank you for all of your comments. I was starting to feel like maybe my expectations were too high and I was being unreasonable with the contractor. I found this company through Service Magic so I'm going to file a complaint with them and see what my options are. I really don't think these guys have the skills to fix the tile.

Looks to me like they didn't clean the grout before it hardened. Once hardened, nothing can be done to "clean it up" except remove it and start over. Grout hardens pretty fast, you can only do about 5-10sq feet before getting serious about cleaning (most has like 20 mn working time). I've seen people mix up too much grout, then appy it all, and by that time it's now too hard to clean and smooth the grout lines. Either the person was using a grout that they were not use to, and it hardened up way faster than they expected, or the person was very inexperinced.

BTW - the obvioulsy have no clue how to apply caulk either. Some of the worst tile jobs I've seen are in fast food bathrooms - but yours is one of the worst I've ever seen. Like other said, it's not even remotely acceptable.

I saw you mentioned Service Magic. I hear people use that service all the time, but I have Angie's List. One day I decided to test out Service Magic to look for a carpenter. Well, all three of the carpenters were also on Angie's List, all with a low rating. That's just my experience.