If the puck is a bit wet that's not necessarily a problem as long as your extraction is fine. As I understand you are still able to pull the shot, so clogging as suggested is probably not the reason.
The reasons for pucks to be wet is most often that the space between the puck and the group head is too big. When you start pulling the shot, the water is pumped through the group head onto your grounds, filling up the space between the head (more precisely the metal filter) and the puck. The pressure then pushes the water through the grounds, extracting the coffee. When you finish the extraction process there's obviously still water in this chamber and if it's too much it will wet the puck into the sloppy mess you are referring to.
It could be that the basket you are using is too big for the shots you pull or rather that you use too little ground coffee. If it's a single basket you should use about 9-10g of coffee for an espresso with a yield of about 18-20g. However as I said, it's not really a problem if the extraction is ok and the espresso tastes good.