You should review the rules and regulations for the HOA. That's where you may find your answer. If you do not find anything about a casual observer, etc., you may have good grounds of challenging any future citation. I wonder if you and others started making a million complaints about people with allegations if this practice would stop? What if you saw this homeowner driving and estimated his speed to be faster than the speed limit and filed a complaint with this person? If this person didn't get to use a radar gun etc, your claim should be taken seriously against this accuser.
This response does not create an attorney-client relationship.
Yes. In California, an HOA can issue speeding tickets and fine for speeding and/or reckless driving. HOAs have the authority to make and enforce rules for common area use. If the HOA receives information about speeding or other violations, the HOA should investigate and determine whether a violation occurred.
Before the HOA can impose penalties, the accused is entitled to "due process", which means notice and a hearing where the owner can offer his/her version of the events. Since homeowners are entitled to challenge information about the alleged violation, the HOA board cannot rely on anonymous reports.