Errr, if the charge is common assault it can only be heard by a Magistrates. If I have understood your previous post, you have been found guilty by a Magistrates Court. Consequently, they must have been sure of your guilt to convict.
You can appeal to the Crown Court, but there is no guarantee it will get "thrown out". The case will be a rehearing of the case in the MC, and if the Judge and two lay magistrates are sure, they will also convict and your appeal will have been unsuccessful.
I cannot see that your legal team have done anything wrong.