You need to either use a cable spool dispenser to unravel cable without twisting, or use a home-brew method such as suspending the cable between studs on a broomstick to unroll it. Pulling the cable off a spool lying on the floor will guarantee the cable will be twisted every time. The spool has to rotate as cable is being peeled off for it not to twist.
To answer your original question, there is nothing physically wrong with having twisted cable, but as you infer, it sure doesn't look very professional.

That said, as BB said, there is nothing wrong or illegal about the twists, as long as you staple them on the flat.

$2 Wire spinner:
take two pieces of 2x4 a couple of inches wider than a roll of romex. Nail or screw (preffered) the two pieces to make a T shape. Take a piece of romex long enough to go from one side of the T up and over the center 2X4 to the other side of the T. Staple at all three ends and under the two sides. When you hold the T upside down it will look like two right triangles with the wire being two of the sides. Take half of a cold water ground clamp and drill a hole through the center. Run a nail through the center and bend it over enough to form a hook. Screw ground clamp to the top of your upside down T. Drive a staple halfway in a ceiling joist, slide roll of wire onto the spinner and hang from staple. Wire comes off straight with a tug and weight of the wire will keep too much romex from unspooling unless you really give it a tug :)

Making one that works is easy, as already described. For a picture of one, try the link.

Here is a link that might be useful: Reel

I am not using a spool of wire, but those 250' romex coils wrapped in plastic shrink wrap, there is no spool. If I remove the shrink wrap, I may have a mess. I have been removing the wire from the center of the coil with the shrink wrap in place.

Matt,

FWIW, I used up a 250' roll of #12/2, packaged as you described, just week before last and didn't have a wire spinner or spool dispenser available.

What I do is get rid of the wrapper and take wire from the outer circumference. While it is possible to make a mess of this, it's not that likely unless you let the inner end of the coil get untracked.

If I'm working by myself, I take wire off of the coil by temporarily securing the end to something (including, for example, a stud hole where the cable will run) or put a cinder block on it. I then act as my own spool by holding the coil vertically and walking backwards, turning the coil as I go.

If you're doing a lot of wiring, it's much better to build or buy a proper spool or spinner, but if it isn't that big a job, I've found it easier to "walk it out" rather than try to untwist all of the kinks by hand.

Even better, enlist an assistant and give him/her about 5 minutes training and practice in how to "play spool". Even a 12-year-old boy can learn to do this pretty quickly. Wives might also work, but that could end up costing you more (one way or the other!) than a spinner. :-)

The link I provided pictures a reel that will accommodate the 250' coil. Drop the coil on the reel, remove the shrink wrap and start pulling the cable from the outside. The reel rotates.

Take the roll out of the shrink wrap and unroll as much as you need from th outside of the roll. If you have a bunch of twists it just say "Hack". Do it right and you will have a job to be proud of, leave all the twists and you will just have another crappy do it yourselfer job.