I thought it was against the law to give bad references, yet every series there seems to be at least one highly critical comment passed on to the interviewers from the candidate's past employer. This year one was criticized for not being a 'starter and finisher'.

Not sure its against the law, but you could sue for libel and then the employer would have to prove what they said is true.
Hence the advice now is to simply stick to easily verifiable stuff like time keeping, sickness.
Of course in 'The Apprentice' the circumstances aren't really like that in real life anyway.

References are a minefield for an employer and could leave them open to being sued if they cannot substantiate what they have written or if it created a misleading impression. There are lots of ifs and buts; however, in short, the legal position is summed up here:

You owe a duty of care to the ex-employee in providing a reference to a prospective employer. Your duty is to take reasonable care in the preparation of the reference and you will be liable to the employee in negligence if you fail to do so and the employee suffers loss or damage as a result.

I'm guessing the participants must contractually agree to getting bad references for the purposes of the show.

Yeah, I think the application form asks which employer would give you the worst reference.