Red wine contains histamine. That can cause migraine attacks or other types of symptoms that occur from a histamine intolerance. Furthermore, the disadvantages also depend on the amount of wine you drink. One glass a day should not cause you any negative effects, however it's noteworthy that red wine, and alcohol I general, has empty calories. Basically, this could be stopping weight loss, but only if you consume it in large amounts. Other than that there’s the general risks as with alcohol, that it may affect your judgment, slow your reaction time, you should never drink and drive and that you could get addicted of it. However all of those will, in the majority of cases, not occur with small amounts of alcohol/red wine. Remember, do not drink and drive.
To sum up, there's more advantages to moderate red wine consumption than possible disadvantages. You should find a good amount for you, taking into consideration the different standards around the globe, such that: (US) 1 glass a day for woman, and 2 glasses a day for men (Europe) 2 glasses a day for woman and 3–4 glasses a day for men. Those are only proposed limits, and each one should set their own, appropriate limit.