Actually dragging the behind like that usually indicates a problem with the anal glands or sometimes an irritation of the anal area because of stool stuck on skin or coat there.
You can read about anal glands here
http://www.marvistavet.com/html/body_anal_sacs.html
Usually when a dog has worms or coccidia or giardia etc the vet checks a stool sample under the microscope because the signs in the stool are normally eggs or oocytes not adult worms.
You can read about worms here
www.thepetcenter.com/exa/worms.html
and protozoans like coccidia and giardia here
http://www.lbah.com/intpar.htm#coccidia
http://www.lbah.com/intpar.htm#giardia
While you do sometimes see a worm in stool or vomit mostly they stay safely inside only shedding eggs to pass on to other animals.
It may be the red dots are from flea bites or mosquito or fly bites. They could also be a sign of a mild skin infection. You can see if a chlorhexaderm shampoo from the pet supply store will clear them up.
Hope this helps you!

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