Bear in mind that the primary job of the staff is to follow the policy from above, really. There is a lot of administrative work and in my experience it's tedium in absurdum. Current JSA guidelines place a lot of emphasis on the claimant finding work, signing on to various agencies such as Reed Employment and making regular job searches and applications. Usually the only thing that someone at a Jobcentre adds is that they perform these searches for you, but if you are competent around a computer and the internet, there is little or nothing they can add to the process. This isn't really their fault, but in a way the job-searching stage isn't all that difficult. Find something in your area that you can travel to, for which you have the right experience and qualifications. It's the rest of it that's tough, and yet there are also plenty of CV-writing guides out there, too.
When I was on JSA last Summer, virtually the only thing I needed to go to the Jobcentre for was to sign on. If you know what you are doing then the advisors there do become redundant -- but that's not really their fault.
As to your specific problem, it depends on the timing I guess. If you were not made aware of the Avanta appointment before you missed it then you have reasonable grounds to challenge the decision but hopefully it can be sorted out rather easier than an Appeals process. Show them the letter and all will be well, I hope.
Being on JSA is a headache, I'm afraid, so hopefully it won't be too long before you find a new job and you can get off it.