Can't think of any cons really - depends on what you want to use it for. Ours was here when we bought the house, and I have to admit was a real selling point for us. We have a couple of futons in here too - and a small portable TV with DVD so when our DDs have friends over they can watch a film, and then sleep out here.
Ours has double doors, opening windows and a porch area. Great for thr Teens to hang out in, and for visiting small people to play in.
The downsides are it is soo far from the house, so when entertaining you have lots of trips to the kitchen, but it is cosy with a BBQ or Chiminea outside. We have had electricity installed so can have heater & have electric lights.
Late last summer the kids had a disco at the bottom of the garden with disco lights in & around the SUmmerhouse (we have no neighbours at the back - it's a cemetry).
we have one, it's big, and yes, it does harbour quite a few spiders and earwigs etc. dh fitted an air conditioning unit, keeps it heated in winter. we don't use it as a summer house though, dh is a portrait painter and it's his studio