I am in two minds about this idea. There are good and bad sides to it.

"Pupils at a Leicester school once named as the worst performing in England are now helping to decide who should teach them.
Students at New College have started to sit in on job interview panels for all new staff.
The policy is part of changes which saw the school come out of special measures in 2006...
Two or three pupils are picked each time from a dozen members of the School Forum to take part in the recruitment process, taking it in turns to quiz prospective staff." (BBC)

Having children on the interview panel could help select the teachers with an attitude that the children would like and which could help improve their learning experience. It could also mean that the children are more receptive to the teachers they help choose and behave better for them.

However, giving children that sort of power over selecting their teachers is not necessarily a good thing, certainly not in all aspects. Children are going to look very much from a specific viewpoint, and often the teachers who school children like most are not the ones from which they learn the most, but the ones who let them muck around in lessons and the like. But on the flip side of that, if they enjoy the lesson, they also tend to be far more receptive to the learning part of the lesson.

A large problem with giving children a say in the choice of teachers is that it can give them power over the new teacher. Whilst this may be relatively minimal when it comes to appointing external teachers to a post, if there are any internal applications for teacher jobs, that could certainly lead to providing pupils with power over their teachers - not a good thing in a situation such as a classroom.

I am certainly not convinced that this is a unqualified "good thing". But there are certainly some obvious potential gains - depending, however, on the manner in which the children are involved. How much say do they have? Are they there to offer opinions as to the "best" teacher from the applicants or to provide feedback on what they think of each individual regardless of the competition? So long as the role of the children is purely advisory and primarily as a means of assessing the reactions of the applicants to the children and vice versa rather than giving the children a specific choice of teacher, then it appears to be a good idea. But if it extends much beyond that, it threatens to change the dynamic of the classroom, with the children having power over the teachers - and that would certainly be a bad thing.

Source: BBC