There will always be some "puddling" on the tops of mugs in the dishwasher in my experience. This is because they have a well on the end of the cup, so the water really has nowhere to go (unless you have the super duper super dry function which most don't have). If this is the only thing not drying, I wouldn't worry too much. Get a bit of kitchen towel and wipe the offending tops before taking out.
Plastics in the DW don't dry too good, so I wouldn't stress about that either, paper towel again.
If it is the case that cutlery is dripping and the stuff on the bottom rack is really wet, then I think you might need to get someone to have a look at it for you.