If you're playing by USA Ultimate 11th Edition rules:
the thrower may call a technical time-out during play to replace a cracked, torn, deeply gouged, creased, or punctured disc; a warped, wet or dirty disc does not qualify
Regarding what disc you can start the game with:
Any disc acceptable to both team captains may be used. If they cannot agree, the current Official Disc of the Ultimate Players Association is used
Official competition discs are listed here: http://www.usaultimate.org/resources/disc_standards.aspx.
If playing by WFDF rules:
The thrower may call a technical stoppage during play to replace a severely damaged disc.
"severely damaged" is not defined.
Teams may choose to start the game with any disc acceptable to both captains.
In WFDF competition, discs must:
- A. Have a saucer-like configuration with a non-perforated flight plate and an inner rim depth (that portion of the rim that is generally vertical to the flight plate), which is at least 5 percent of the outside diameter measurement;
- B. be made of solid plastic material, without any inflatable components;
- C. have an outside diameter measurement of not less than 21 cm nor greater than 40 cm;
- D. achieve a rim configuration rating of 26 or greater (see section 108[D]) ;
- E. have a leading edge radius that is greater than 1/16 in (1.6 mm) (see section 108[E]) ;
- F. not exceed 120.7 N (12.3 kg /27 lbs.) of pressing force as measured by the flexibility testing procedure (see section 108[F]) ;
- G. weigh no more than 8.3 gm per cm of outside diameter and shall weigh no more than 200 gm regardless of size;
- H. be essentially as produced, without any post-production modifications which affect weight or flight characteristics;
- I. present no unreasonable danger to players or spectators;
- J. be a production-type disc available commercially to the public in numbers of at least 1,500 and,
- K. be specifically approved by the event director if questioned by any player in the contest, but in no case will the disc be approved if it is in violation of any of the above specifications.