I personally have a drink every so often, but I make sure not to let it get out of hand because I've what alcoholism can do to a person.
That's a wise decision. Alcoholism is a term for drinking excessively and causes mental and physical health problems.
So can the alcohol itself cause any physical or mental issues that are unique to purely alcoholism compared to, say, addiction to heroin or other drugs?
Yes, alcohol particularly affects the brain, heart, liver, and pancreas. The first organ that is typically damaged is the liver.