Blood clot in the arms does rarely occur. If it happens in arms, it is called Paget-Schroetter disease, a Deep Vein Thrombosis (DVT) that occurs in the upper extremities. Deep vein thrombosis is sometimes asymptomatic although it is usually painful, swollen and feels warm to touch. Any person who develops this condition should be checked immediately by the doctor since the blood clot could travel fast into the lungs and can lead to pulmonary embolism which can be fatal.
A blood clot that forms inside the arm can cause blockage and poor circulation if its not dissolved quickly by body's mechanisms. It often forms in the vein because of its higher caliber and lesser hemodynamic pressures. A clot in the arm is called Paget-Schroetter disease, symptoms include sudden pain, warmth, redness or blueness with swelling in arm. It is an emergency. Here is a link about the condition: http://www.ask.com/wiki/Paget-Schroetter_disease?qsrc=3044