I believe I saw some cables stapled (!) to a backing board. If they are "cable staples," it probably not a big deal, if they are traditional "flat top" staples, it could be a bad thing ... not necessarily a killer, but definately out of spec.
Cable staples are arched so that the staple doesn't actually compress the jacket of the cabling (the spec says "no compression of the jacket" - in many UTP cables, that interferes with the lay of the pair within the jacket and reduces (to some degree) the anti-crosstalk / noise rejection properties, and may cause an "impedence lump" (and area of radically different impedence -which is the resistance a cable presents at a given frequency- which can degrade the signal). Staples also make it difficult to replace a cable if it's found to be fubar after the walls are up.
As Cmetz mentioned, overall, it's not a bad job. Most of the better cable offer a little headroom (performance above spec is what I mean) that gives the installer some latitude from a "perfect" install. Try to get a certification scan on paper from the installers, make copies, and keep it in/on/near the panel. Someday when you want to sell the place, you can show the prospective buyers that the cabling was professionally installed, and that it meets a certification spec.
If the installer can't / won't do a scan, then bring in an outside data-cable installer that will, get it on paper, and if the cable doesn't meet cat5e spec (as presented on the quote), then get it fixed (the installer should pick up the cost), or get a refund.
Congrats! "real" cabling give you many options beyond connecting computers. There are adapters for transmitting video, audio, serial ... almost any kind of signalling.
FWIW
Scott