Hello Gary,
I use various acrylic polishes on the exterior (depending on the depth of the scratch and/or the type of smudge), then rinse with water, pat with a soft cloth, blow dry and the final step is to polish the dome with Lemon Pledge. The techs at Aquatica use it and the Pledge has been a great, quick polish to carry with me. I often use it in-between dives, after the port has been rinsed and dried.
For more serious polishes, I suggest you try:
http://www.micro-surface.comDebbie Abrahms is the contact. Tell her I suggested that you give them a try and that you are an underwater photographer. She will send you a sample kit. Between trips, I often take an electric, rotary hand polisher and add some Micro-Glaze. It can work wonders on an "experienced" dome.
Scott Johnson
SeaScapes Images