One thing that we did when I was showing in 4-H with a friend was we had a set of brushes we only used for shows. We did this because we both had grey horses and any dirt left on the brushes from brushing a horse when it was really dirty seemed to get on the horse. Using the clean brushes seemed to help. It also looked more neat to have a set of brushes rather then a bunch of mismatched brushes.
Also showsheen helps but be careful because it makes the saddle slip like people said. Showmanship was always the first class so we sprayed the horses with showsheen the night before and it made them shiny but not too slick. Then after showmanship we tacked up our horses then sprayed them with showsheen (so we didnt get any under the saddle). The showsheen made it so dirt that got on their legs from the practice arena would be easier to brush off.