Warfarin is not known to have any negative effects on positive side of the male function. And priapism is not common with warfain at all (thank goodness!), nor with the many other drugs that can supposedly cause it: sildenafil (Viagra), tadalafil (Cialis), vardenafil (Levitra), papaverine, fluoxetine (Prozac), bupropion (Wellbutrin), risperidone (Risperdal), olanzapine (Zyprexa), and heparin.
The phrase "blood thinner" is a medically tolerated term only because it has been in the common vernacular for so long. It's just more vividly "understandable" and easier to say than "anticoagulant." It just seems impossible to get it out of the language. As such, many professionals have given up the attempt and just refer to warfain, heparin, and various other anticoagulants as blood thinners, just so a majority of people will know what they're talking about and listen to what they're saying. Many people just stop listening if you use terms like anticoagulant.
As Kristy pointed out so well above, none of these products actually affects the viscosity of your blood. It's just as "thick" as it was before. It looks the same, smells the same, tastes the same. It just won't stick to itself and form a clot (coagulate) as quickly as it did before. Like wintering over gas in a mower with Sta-bil or another stabilizer in it, instead of without. The gasoline looks, works, smells, burns the same, no thicker or thinner, but it just doesn't clog up the carbureter.
Best wishes,