Definitions of Defects
Hard and soft cover books:
Darkening or Fading Tanning or color loss due to age or sun exposure.
Foxing Dark spots, fairly common in books that are very old or printed on lesser quality paper, and greatly exacerbated by exposure to light, moisture, and/or soil.  Tends to appear first on edges and end papers.
Rubbing Can range from small wear spots affecting only gloss to material loss.
Shelf wear / edge wear The loss of gloss, color and/or minor chipping resulting from handling.
Bumps Any damage caused by impact with another object.  These are common to edges and corners.  Bumped cover surfaces are more visible viewed at an angle to the light.
Dog Ears Corner of a page is creased.  Often this occurs with improper storage or handling, and some people dog-ear pages in order to find where they left off reading.
Chipping The loss of small bits of paper, usually along edges.
Brittle The paper is dry and delicate due to age or exposure damage.
Warp Wavy distortion of the cover and/or text block.  Water damage.  Sometimes caused by damp storage conditions.
Slant The spine (and therefore the text block) is leaning;  the binding is not at a right angle to the covers.
Binding errors Text block not centered inside covers, boards at odd angles to the spine, wrinkles in cloth or paper covering, gutters too short or too loose, pages out of order or upside-down.  Errors are often corrected early in a print run.
Loose Hinges are weak, or pages are starting to come loose from the binding.
Broken The binding is cracked or completely separated from top to bottom, parallel with the spine.  The book may look fine when closed, but the signatures or glued pages are not all properly held together.
Split The binding is partially cracked, but the signatures or glued pages are still holding.
Loose or Shaken The binding is whole, but some or all signatures are no longer tightly bound together.
Sticker Ghost Residue, discoloration, or other plain evidence that a label has been removed.
Sticker Peel Label or price tag removal damage with surface color or paper loss.
Bookplate Label affixed inside a book identifying the book's owner, often decorative.
Inscriptions Written name, address, date, and/or message, usually on the FEP.  Often considered an attribute if written by a famous or important person.
Writing Names, inscriptions, notation, marginalia, doodles, or the highlighting or obliteration of original print, done by hand with any stylus.  Often but not always considered a defect.
Stamps Ink or embossed marks imprinted by a book store or previous owner
Remainder Marks Unsold overstock is often marked by the publisher, usually with an ink stain to the edge of the text block.
Tape Repairs Tears or paper loss repaired with adhesive tape (-don't do it!)
Cup Rings Visible on the covers of books carelessly used as coasters (don't do that either!)
Softcover Specific Defects
Stress lines/ Reading Creases On or directly adjacent to the spine, these can be barely visible, or a severe crease resulting in loss of color, legibility and integrity.
Binding errors Cover off center, improperly glued causing wrinkles, warp, or buckle.
Roll / Rolled Spine The spine is bent lengthwise and is not at right angles to the covers.  This type of curvature is very common in larger or older used copies;  This happens to hardcovers that are large or have glued bindings as well, but it applies to the binding, not the spine portion of the casing, and so is less noticeable.  I haven't noticed this term used to describe hardcovers.
Lamination Lift Older and oversize paperbacks often have laminated covers.  This tends to peel over time.  It can be a minor flaking or total loss of lamination, most common along the bottom edges.
Color Flaking This is the loss of small bits of color from the surface of the paper, which is not significant enough to call chipping.  Paper is bare but otherwise apparently undamaged.
Corner curl One of the corners at the fore-edge does not lie flat.  May mildly affect only the cover, or may include a large part of the text block.  Pages may be so curled that they fold over onto themselves multiple times.  This does not usually affect readability.
Punched cover Actual hole punched in the cover, indicating a discounted book.  A practice often employed by book stores to indicate a non-returnable book.
Corner clip The removal of a triangular corner of the book cover, also indicating a discounted and / or non-returnable book.
About Dust Jackets
These are sometimes just plain printed paper book covers, sometimes glossy or printed on quality stock (and are therefore more resistant to soil and tears).  All are subject to any damage that applies to pages or soft covers, and more so.  They begin to degrade immediately - most have minor shelf wear before they leave the bookstore.  Common faults are edgewear, rubbing, chipping, fading, creases, stains, and tears.  Dust jacket tears are often tape repaired.  I have not seen a published grading standard for them, but I use hardcover book grading terms, and call any jacket that is whole with minimal edgewear and very few very short tears very good.  The best way to preserve a dust jacket is to put it in an acid-free clear cover;  I use these.  If you collect books, love books, or might want to re-sell them some day, the jacket is worth preserving.
About Slipcases
Slipcase damage descriptions are most similar to those for book covers, since they are usually paper boards covered with either paper, or the same material as the books they protect, and are also made to save books from wear.  Common faults are rubbing, shelf wear, bumps, stains, age discolorations, and splits.  A split in this case is a tear of any length along any edge;  a box is said to be broken when it is not functional.  Splits are easily made worse with handling, and so are often tape repaired.  Slipcases are often highly decorative, and sometimes are even the most collectible piece of a set.