This joke is based on the double meaning of spotted.
Dalmatians are white dogs with black spots. The Dalmatian dog in the cartoon has black spots on his body. When something has spots on it, we can say it is spotted: he is a spotted dog.
"The man painting the wall has spots of paint on his clothes."
"She bought a spotted dress to wear to the party" - the pattern of the dress has spots.
Spot can also be used as a verb meaning to notice, find or detect something.
"Read this report and see if you can spot any mistakes."
"I finally spotted my friend in the crowd."
"They couldn't spot her because she was hiding."
