What happens if someone gets a 6 month visa visit, stating in the application that they will stay for 1 month, but then stays for 4? I presume they will get some sort of black mark against their name that will affect future applications. Does the sponsor get a similar black mark that would affect anything other than sponsoring that same individual?

No black marks as such, but it will be taken in to account when determining any subsequent visit visa application.

Are you planning to sponsor someone else? It wouldn't technically be an overstay if the person stayed less than 6 months anyway, so no black mark.

Staying longer than originally stated/intended would not legally be classed as overstaying. However, as Scouse says, it can through up doubts about the applicants sincerity or integrity. On any subsequent application the applicant should provide a reasonable explanation ("I felt like it" wont do).

However, if the applicant was asked to sign an undertaking to return within a specified time limit and stayed longer than this, then the explanation would have to be very convincing!

Circumstances can always change. In any event, the enforced signing of undertakings to limit an applicant to a certain amount of time in the UK after a visa has been granted is of dubious legality.

....the enforced signing of undertakings to limit an applicant to a certain amount of time in the UK after a visa has been granted is of dubious legality.

And they're not worth the paper they're written on. Believe it or not, the UK used to make Libyans sign such declarations to the effect that they promised not to seek to blow anything up whilst in the UK. Did they really think that a potential terrorist would be dissuaded from violent acts because he'd signed a little chitty?

Scouse.

^ Astonishing. You couldn't make it up, could you