Ask for feedback. Consultants interview hundreds of people. They should be able to give you one or two pointers, and, if they are presenting you to their clients, it's in their interest to do so.
Sometimes consultants will not present you and will not tell you why. A good consultant will tell you why they won't. A poor one will leave you hanging.
It's often worth asking this to find out if the role is a new one or you're replacing a leaver. If the role is new, it could mean the company is expanding, which indicates they are financially stable. However, it also means there could be some trial and error if no one has done this particular job before.
This gives you a sense of what may be available within a company. If the last person in the role was promoted, that's probably a good sign.
You want to appear to fit in with the company culture. If you dress too smart, you could be out of synch with the interviewer and the company; too casual and you'll risk appearing slovenly or unprofessional.
This can open up a franker discussion about your quality as a candidate.
With these questions, you get a sense of your worth in this equation plus how long it may take for them to make a decision about you.
I emphasize asking "you." That brings the question back to their opinion, not what is written down in a job description. You may get a deeper insight that way. A consultant who is not familiar with the client, will probably refer you back to the job description. This should serve as a warning sign to do your own due diligence on the information they provide.
A good consulting relationship takes time to build. So you will want your consultant to at the very least have visited the client. If a consultant works for a long time with a client, they should know more about what makes the organization tick. However, sometimes the consultant's dealings with the client may be speculative. They may have called the client and suggested they have good candidates, then advertised. If you get a sense that this is the case, then you will need to ask more questions of their client before you make up your mind about a job.
What's their role in the hiring decision? Sometimes there will be two or three people interviewing you at various stages. Each has their own role to play. You need to establish what that is so you can prepare properly.