The bad taste left after drinking wine can be attributed a number of agents found in wine, particularly alcoholic wines.
Alcoholic wines typically contain 8-15% ethanol. When ethanol mixes with oxygen in air it gets oxidised, gradually producing acetic acid (vinegar).
Furthermore, the reaction of ethanol with urea (naturally present in wine) to form ethyl carbomate (urethane) can produce a saline, bitter taste, although probably not toxic.
The ethanol in wine is produced through the fermentation of carbohydrates by yeast. This process also results in the production of acetaldehydes which contribute to its complex set of flavours.
Ethanol itself however is tasteless. It is however toxic and a class 1 carinogen according to the International Agency for Research on Cancer (IARC).
When consumed, ethanol is oxidised by alcohol dehydrogenase (ADH) enzymes in the body to produce acetaldehyde, which is 10-30 times more toxic than alcohol and possibly carcinogenic in humans.
Recent scientific research on cancer seems to indicate even low levels of alcohol consumption (1 cup per day) 'increases the risk of cancer of oral cavity and pharynx, esophagus and female breast' Source: http://annonc.oxfordjournals.org/content/early/2012/08/21/annonc.mds337.full
So a bad taste may not be the worst thing alcohol leaves in one's mouth.
With regard to the health effects of alcohol, please refer to the World Health Organisation report which is based on data collected scientifically from around the world over many years.