Those don't sound "too bad" but ... those could also be famous last words. I don't really know much about that sort of thing but I do know that small movements (as in jacking a floor which I've done in the past) does cause cracks to open up.
IMO, you should first: Create a reference and get pictures of the cracks. If a nail sticks into them, stick the nail in for the picture. Try to measure and write down the sizes, length of width and direction of each crack and note its location. You'll then have a "reference". If the cracks change over time or new ones occur, it could be really good informaiton to have on hand. Sometimes just having a reference like that is enough to talk a contractor whatever into taking care of things, IF they need to be taken care of. The worst part of this sounds to me like you were surprised by it. That never should have happened. You should have been advised of that sort of thing. Surprises are never good on any job.
The bit about No Permit is a little disconcerting, too. I'm pretty sure one was needed, but ... like I said, no expert here. I'd call the local code enforcement office and ask if a permit is needed for that sort of thing - you don't have to identify yourself just to ask a question. Then, assuming one was needed, I'd ask the contractor for a copy of it for your records - a completely reasonable request. The permit should have been prominently displayed while the work was in progress. I've no idea whether inspections were required when the job was finished, but ... I would think that was the case.
For sure, create your reference point as I mentioned above, and then go after the rest of it. Do NOT jump to conclusions because this whole thing might be a whole set of tiny details not worth worrying about. But do find out ,just in case it IS a big deal, about the permit situation because that could really bite you in the ass in the future. I'll be very surprised if no permit was required to do that sort of work. Was the contractor bonded/insured?
HTH, Pop