Should I skin the common sole for pan?
I would say it's totally up to you.

I prefer it with the skin still on, it get's really juicy inside. However it's a bit more difficult to eat. So perhaps if you were making it for kids (although, you could just skin them after they are fried), you could skin it.

One opportunity I really think is better without skin is when you serve it with sauce. Having to fiddle around with the skin covered in sauce is not really handy nor fun.