Some assumptions of basic secret sharing (say Shamir) that may not be fulfilled in practice include:
Honest Dealer: This has to do with trusting a third party. Verifiable secret sharing was introduced [1] to ensure that even if the dealer is malicious there is a well-defined secret that the players can later reconstruct.
Honest Parties: It is easy to see that if a malicious participant (who holds a share) submits a false share while all the rest of the users submit correct shares, the malicious party can learn the secret and ensure the rest will not learn the secret.
Other wrinkles/improvements include (for example) computationally secure secret sharing [the Shamir scheme is information theoretically secure but less efficient] multi-secret sharing, space efficient secret sharing etc. The topic of secret sharing is within the broader topic of multiparty computation. You can easily find out more about these topics online.
References:
- Chor, Benny; Goldwasser, Shafi; Micali, Silvio; Awerbuch, Baruch (1985). "Verifiable secret sharing and achieving simultaneity in the presence of faults". 26th Annual Symposium on Foundations of Computer Science (SFCS 1985): 383–395.
